I don't know if this is helpful (though it's probably more helpful than "get an officially supported phone") but my Blackberry Bold is working great with my MobileMe mail. Strangely enough, it actually pushes faster to my BB than my GMail account!
Maybe try resending the service books (highlight your email account in EMail setup and hit the menu button, then "Resend Service Books").
If that doesn't work, try deleting the account, rebooting your phone, and adding your account again.
Sometimes the service books get corrupt and that can cause non-delivery.
Also make sure to go into EMail settings and check to see if "Send Email to Handheld" is checked - that burned me once!