My guess: it would be more work to take it out than to do nothing.

But why do they not hide the interface directly?

because it's not hurting their user acquisition by giving users the option to directly invite people, even if it's open for all.

From my experience, and I may be incorrect, if you invite someone from Gmail they do not need to verify the account via an SMS message.

My guess: for those cases when you want to invite someone. You could either tell them "just click yourself through mail.google.com" or send them a ready-made link in one go. Some people may prefer the latter.

I think this is reasonable.

My guess: Gmail wants you to invite somebody in your contact list directly. And they are reluctant to reset the cap of invitation because there are so many users in the system.

why not just remove the line '50 invites left' and substitute it wit something better like 'invite someone'

Probably to stop spammers taking advantage of it. Invitees don't need to verify their accounts, so a spammer could make 1 legitimate account, and then invite themselves a few hundred times for instant new verification-free spam accounts.

Just a guess.

The illusion of limited supply makes Gmail accounts appear more valuable even if you're smart enough to realize that's not the case.