OP I am training at an an academic site, and honestly, sometimes I wish I trained at a community site because my impression was that it was less consultant heavy. Your experience sounds atypical.
We also end up consulting on way too many distal radius fractures instead of just reducing on our own. I agree with you, it's really difficult to be an ED doc and have to stand aside and watch a consultant put in a chest tube. It's happened to me a few times and then they come and get you when they want you to order a CXR. It's the absolute worst.
People will tell you all sorts of advice on how to handle this issue, and I can tell you for a fact that most of it is incorrect. Asking a consultant if they will let you do the procedure NEVER works. Even if they agree to it, they will inevitably end up taking over the procedure. Them "showing you" ends in always in them actually doing it. And honestly, I don't blame them. If you are consulting a service, especially if it's another resident, they are going to do the procedure. They are the ones who are going to be held accountable for the outcome. It's very rare for a ortho resident to let me do a reduction and "teach me" when they are going to get chewed out by their attending if it's not perfect.
The solutions:
1) You need to get support from your attendings. If you aren't getting it, you NEED to tell your PD and raise hell about it. If there is a procedure I want, I will tell my attending and most of the time they will fight for me to get it. If you don't have your attending on your side, it won't fly.
2) Try to convince your attendings not to consult. This is hard to do, and many of them are stubborn, and they don't want to deal with a complicated reduction, lac repair etc. I tell them that I want to do the procedure, I ask them to teach me how to do it so we don't have to consult in the first place. If they aren't going to do it, again, raise hell with your PD
3) Do the procedure, then consult the specialist. This one has gotten me into trouble a bunch of times, but sometimes it's how it needs to be. For instance, I got pissed that I wasn't getting enough distal radius fracture reductions. So I did a hematoma block and reduced it. My attending being lazy and overly conservative felt uncomfortable with that, and requested I consulted ortho. I consulted ortho and they were really upset that I had done a hematoma block (couldn't get an exam) and did a reduction already. It's poor form honestly and I don't think this is the best way to do it, but I made it very clear with them: if you don't want me doing the reduction before calling you, then you need to teach me how to do these so I am ready when I go into community practice and you aren't there. Ever since then I have been getting more procedures.
To be honest, things like ortho reductions are bread and butter and we need to be good at them. But you HAVE to get your airways, chest tubes, central lines etc because those are critical life saving procedures and your program should not be letting people take them from you.
You have to advocate for yourself and be aggressive about it. But you also need some buy in from your attendings and residency leadership. If you aren't getting it, be vocal about it. Ask your co-residents what experiences they are having. If they are having similar issues, again, bring it up with your PD, you guys will have more power in numbers. When you fill out your ACGME surveys, dock your program points in these issues, they will be forced to address it otherwise they will go on probation.
Good luck
edit: regarding your question about county programs... I don't think county programs are having residents just getting all these thoracotomies and chest tubes. county programs offer great training, and sometimes they have very sick patients, but sometimes they have very low acuity patients who are just looking for a bed to sleep in. Community places I would argue are a great place to train because you get a good combination of high acuity patients, less consultants. You are probably at a good program with a lot of good pieces in place but you need to make your voice heard with your residency leadership that you need their support.
edit2: MOONLIGHT. MOONLIGHT. MOONLIGHT. Take every opportunity to do this if you can. Don't waste your time being chief resident and getting caught up in other BS, moonlight for the experience in these procedures, not even the money.