Broken iphone screen/ backup/ iphone data transfer

It is my humble opinion that apple needs to develop a recourse for an iphone with a broken screen in regards to transferring it's data to a new phone.

Even at the Apple store they have no way of unlocking an iphone via computer without use of it's screen. The only hope or alternative is to have the screen replaced for $150 and hope that the data isn't wiped in the process.

It seems to me that apple could develop some sort of proprietary software used exclusively at apple stores that could do just this - access the iphone just long enough to either turn icloud backup on or allow the passcode to be plugged in as to allow the new iphone to beginning transfer via bluetooth.

I can't be the only one who's experienced this complete and total tedious pain.