My 30-30 has a short throat too. I do not think it is unusual for 30-30's to have short throats, as do 45-70's. I have not shot any factory loads in mine yet, just hand loads. I noticed that I have to seat the 125 grain bullets fairly deep, even 110 grain Hornady's have to be seated rather deep. It sounds like if you are going to be shooting factory ammo, you could use a little throat work. You can send it in for the factory to do, but if you rented a throater, you can do it yourself and get the throat to a custom length. If you send it in, you may get a different barrel back (which may or may not have a short throat), yours with a throat too deep; they even send it back and say there is nothing wrong.
BTW all my other Handi rifles have a long throat, 223, 357 Max (but not as bad as when it was a 357), 44 Mag, 22 Hornet, etc. - too long in my opinion, but that is just the way it is. Good Luck and Good Shooting.