Shelters don't euthanize animals for the fun of it. Also not euthanizing for space, in many cases means that the shelter has decided it has no issue with overcrowding which is a poor medical decision for animals in the shelter. It only results in increased stress to the animals, and increased prevalence of disease.
Limited admission/no kill shelters seem great in the public eyes and make donors very happy. The problem is that they are also serving a very limited number of animals in the community while at the same time demonizing all those other "kill" shelters out there. The net result is the "no kill" shelters get a disproportionately high amount of donations to help very few animals. All while the open admission shelters have fight for donations while struggling to serve the needs of all the other animals that the "no-kill" shelter turned away.
Okay, where to start? Your assessment above has some truisms in it, but it's just an oversimplification of what I see as a really really complex and diffuse group of entities that coexist and provide sheltering services to animals.
Firstly, shelters are all unique and vary widely. The most fundamental and intrinsic characteristics of shelters really come down to three things:
--The community in which they are located, including what other groups exist/compete with them
--Their classification (private, v. public and type of organization), which is closely related to...
--Their primary source of funding
I will touch on the latter two since I think those are more important for comparing and contrasting groups in the same area.
Many shelters are municipal or government organizations, while others are independent, private (generally non-profit) organizations. Government-run shelters are staffed by city/county/district employees, who often belong to unions related to other political unions within that government (sounds like an aside, but that relationship can be very important). They are funded through tax revenue and receive a contract or mandate (usually with the union) to provide X service(s). Municipal shelters can vary a lot in how they operate, how big they are, their overall 'philosophy,' etc.. Most, though, include an animal cruelty investigation component and field services, ie; 'Animal Control.' What is important to remember is the politics/funding/staffing situation that I referred to above.
In contrast, many other groups--shelters and 'rescues' (which are often just a network of foster homes)--are private, non-profit (often 501c3) groups that are completely independent of all other groups. Their staff, if they have any, are not employees of the government, are not generally organized, are privately funded through fees for services and donations.They do not receive a mandate from the government to do anything (apart from perhaps limited agreements with municipalities for dealing with stray animals, but that is an aside). They usually do not have field services, nor do they have a cruelty investigation unit. Usually their philosophy/mission is determined by the board that governs the organization, or the president/CEO-type person at the top... sheltering and providing sanctuary are usually their primary missions.
What are some practical implications of this very basic split between these two general (not exhaustive) types of organizations both getting involved in sheltering?
Well, from what I have seen, there are many key differences:
1. Municipal groups do not have to 'earn' their funding and actually are restricted in how they receive/use donations--often they will have to have outside parties create a separate group and fund to receive donations that then are spent to benefit animals in that facility. Private groups, on the other hand, may receive greater than 80% of their budget through private donations. Consequently, donors have an enormous stake and voice in the organization.
2. A unionized workforce is not the same beast as a non-unionized one. (And here my personal experience will be evident... ) Of course it will be different in terms of labor costs, but also in terms of the working conditions and stipulations that have been and often are written into the working contracts. Work on holidays? Do something outside your narrow job description? Allow a volunteer to do work that fits into your job description? Make changes to the work process that are not negotiated in the contract?? The implications are far-reaching.
3. A government-run, likely unionized organization, is nowhere near as flexible as a privately-funded, non-unionized one and that primarily follows from 1 and 2 above.
I didn't even really touch on the smaller rescues that are nearly one-man shows (except maybe volunteers/foster parents) and that are usually funded in large part by their founder.
Anyways, my final comment on the above is simply that shelters cannot be compared apples and apples when you look at their underlying purposes, the source of their mandate/funds, and the framework within which they can operate on a day-to-day basis. You had better believe this can have an impact on how well they perform in saving animal lives.
Now the next difficult thing is terminology. 'No Kill' is useless. If a group tells you it is 'no kill' all that tells you is that they purport not to kill any animal that isn't considered (and it's by their OWN STANDARDS when you look at the Asilomar Accords) as "Unhealthy/Untreatable." U/U at one place might not be U/U at another place. It depends on the resources at that particular shelter. One place might euthanize an otherwise healthy puppy under 8 weeks old and would classify that as 'U/U" because it is underage. Most progressive places wouldn't dream of euthanizing such a highly adoptable animal that simply needs some veterinary care and time to grow up in a foster home... still others wouldn't even consider Parvo int hat same animal U/U and would treat the animal. All could act according to their own standards and 'claim' to be "No Kill."
In addition, 'open admission' is also a useless term. At one place it means that they won't turn anything down that walks in the door. At another, it means they won't turn the customer down, but they will make them wait for the next available appointment, which might be days or weeks later. Both are really 'open admission' when you look at it, because neither is rejecting animals based on age, breed, medical status, beauty, behavior, etc.. Unfortunately, the terminology that people love to throw around is absolutely unhelpful. ((And I would argue/complain that Maddie's Fund needs to define these terms, but particularly define what the eval codes are across the board for H, T/R, T/M, and U/U. Right now each group can define them as they please.))
How do you measure the performance of a shelter? So many metrics, really... but a couple are considered the 'gold standard.' I would look at a group's intake policies/procedures, consider their criteria for adoptability and how they define the following: Healthy, Treatable/Rehabilitatable, Treatable/Manageable, and Unhealthy/Untreatable; I would take into account the overall number of animals they are serving and look at their Asilomar Live Release rate. There are other things you could look at, too, such as average length of stay, the actual facility, their protocols and procedures for animal care, especially for treatment/containment of contagious disease/vaccine protocols, etc., the role of volunteers, etc..
Add the the fact that many groups actively help one another out by transferring animals in and out of each other's systems, some more willy-nilly than others... it's messy.
In short, its just not simple at all. But please be skeptic and don't just listen to what certain groups/individuals may say--there is a ton of politics within the industry... and it can get really ugly and it isn't always the truth. I definitely think that most groups are more likely to be defensive than they are to admit that they could be doing more and better with the very resources they currently have. Some that are better-managed are set up in such a way that they continually address that issue by reevaluating how they operate with respect to their budget and to the animals they are serving. Others, sadly, are not...
(sorry) So, how many of you have experience working, volunteering or shadowing in shelter medicine? Shelter medicine is an area of medicine I'm interested in, so I'd love to hear about your experiences in the field. 
