I don't shoot Bullseye (or any other type of competitive shooting) but I have read about it kind of a lot here.
You need to look at the rule book but it seems the copy at that site is broken. Get this one
instead. Section 3, equipment and ammunition. It doesn't seem to specify the platform at as low a level as you are describing.
I think the reason 1911's are so popular is tradition...accurizing them has a long history. I don't think there are that many folks who accurize Glocks (just as a "for instance"), and those that do might not be able to get them as accurate as an accurate 1911.