Personally, for signing up I always use my free yahoo email.
I do not use my ISP email because I do not trust them.
I could use email from my domain, but what in case I need to move domain or change hosting.
I don't use my domain emails except for dealing with clients.
And by not accepting free emails you might turn off a lot of newbie customers, and it might not effect someone who can be considered "old timers" (cough*) with the internet.
because from my own experience in registration for service, if the site reject my free email account and request my own domain email address, I'll just give them what they want. (nah! as you want it so much...)
There are a lot of great reasons to do this and great reasons to block them. It depends more on your type of business and your marketing.
For example, what if someone wanted their first domain name and really knew nothing about the internet. There are a lot of people that do not know their ISPs give them several free email accounts. They think that you have to have one from Yahoo or Hotmail.
Yahoo, I think you can look and at least see how long they have been a member, so that should help you some.
And with Yahoo / Hotmail / GMail, even if their ISPs change, these email accounts do not. AOL has just now started to allow you to take your email account with you if you decide to leave (about time - a fantastic marketing idea). Plus using your ISP as your email account, and then if you change and forget your password, you can be in a lot of trouble
Just scrub the transaction a bit more than you usually would since this seems to be a valid concern of yours.