It is my belief that your provider is doing just as Graeme said, and there is a software layer above Exchange (your control panel, I assume) which doesn't provide you with the ability to change the main Administrator account.
I do hope that your provider's control panel admin is separate from the mailboxes themselves. You should be able to delete your ex-employee's mailbox without affecting the control panel, and vice versa.
With the service I provide, my customers have the ability to add multiple contacts to their accounts. They can choose from billing, technical, and contact admin roles. There is only one Account Owner account. HOWEVER, we do allow the customer to change all the Account Owner information to match a new admin's info. If you can't log into the control panel (maybe the ex-employee was the only one who knew the password), all we need is proof that you are the new administrator for your account, and we can reset the password and even make the Account Owner changes for you.
The point is, there are service providers out there who aren't lazy, and provide the kind of service that you want. It might be worth your time to make a list of the things you don't like and what you would want in a hosted Exchange solution, then ask several providers if they can provide those things.