This is a very difficult question to respond to, I'm afraid - as it really depends a lot.
Personally, I cannot speak from experience with America and their providers since I don't know any, although I can only speak with experience from French and English providers - as it took me months and months to find the best provider, allowing me to make hours and hours of calls on a monthly basis and save me plenty, since as is I spend over €1,000 per month on my phone bill.
For France, it also depends. I use Orange Pro - I was given the choice between two options, I can either pay €499 for my phone and use any provider I wish even if it isn't Orange Pro France or I can pay €199 for the exact same phone but it has been modified physically so I can only use Orange Pro France - of course I chose to get that one, heh, since Orange Pro France is the only provider in France and the United Kingdom that were available to me which allowed me to phone internationally, send SMS, EMS, e-mails and even go on the Internet - and it is all taken from my monthly contract. I currently have four mobiles, one with SFR La Carte, one with Orange Pro France contract, and two with T-Mobile United Kingdom Pay-As-You-Go.
I know, in the United Kingdom, with T-Mobile, I need to pay £20 to have my phone unblocked, and I can use then any provider I wish with no hassle. I actually did that with one of my T-Mobile phones when I went to Asia for some business.
So, as you can see it really depends. I know, with One2One which no longer exists, you could only use them and no one else no matter what you tried and no matter how much you wanted to pay them, heh, although then they were bought over by T-Mobile and although service decreased, rudeness became very popular with their staff and for kicks they put on all my letters and documents "Mrs" and various other terms making me out as a woman, they at least allowed me to pay £20 and switch provider.
But, as far as I'm aware, yes the majority will allow you to use whichever provider you wish as long as you pay them a small fee for doing so. However, I advise contacting your provide beforehand and checking, as I said, my latest phone I use for work was actually physically modified by Orange Pro France meaning I can only use them with that particular phone.
Hope this helps. 🙂