First of all, I think that plenty of people on this site think that unsupervised practice of midlevel providers is a bad idea. Also, technically they don't generally practice unsupervised. NPs, for instance, generally have to have some sort of supervision by an MD. A lot of the time, these are unscrupulous arrangements where a doctor charges a fee for supervision and the oversight/educational quality of the supervision is of variable quality. Look around on this site and you'll find a lot of people discussing the topic of NP supervision.
Additionally, there's a few things wrong with the argument that a fourth year has stuff fresher in their mind than a new intern. First, this argument rests on the idea that the main thing that makes a person a good provider is knowledge of guidelines and such things. This stuff is important but there are a lot of things that a new intern will know far better than a new fourth year, such as how to coordinate care between various types of hospital workers, types of community resources, etc. To be honest, being a functional intern relies a lot more on knowing the types of solutions to practical problems that exist in order to effectively problem-solve when a particular problem arises. Most of this you simply learn by seeing patients and it's not a matter of being "fresher" necessarily. To be honest, as an intern, you're also going to make mistakes and this is fine only if you can generally figure out how to fix them. Most of these problems are actually not going to be strictly medically related either.
Also, I do think that there's a sense of ownership over patients that grows in 4th year as you are expected to take a more important role in the care of select group of patients (versus 3rd year where your goal is more to learn as much as you can about the specialty you're rotating in from patients more than it is to actually provide care to them). I mean, in many third year rotations I would be encouraged to "drop" patients when they just became dispo problems and were more or less outpatient level cases residing in the hospital. While this is appropriate for 3rd year, I think it carves out a major potential for growth in 4th year. This is kind of a humbling experience but is important to functioning as a provider. Recently, I had an extremely busy day and forgot to order discharge meds for a patient in time for them to be delivered by the pharmacy runner so that they'd be on the floor for an early morning discharge to a facility. This was entirely my fault and I didn't want it to affect his discharge plan, so I ordered the meds, went down to the pharmacy, paid the (modest) copay out of my own pocket and delivered them to the unit myself. I don't even know that I'd have thought to do this as a third year or early fourth year. As an intern, I did something similar several times where I would pay copays and deliver meds to the floor on the weekends when there were restrictive pharmacy hours and I had an unanticipated discharge. This is just an example but I don't think that as a new fourth year you've been taught the degree to which these things are actually your problems and the extent that you should go to fix them.