|Transferring backup files to the replacement iPhone.|
Apple's tech Genius said that the freezing of the touchscreen was a known hardware problem on the iPhone 6; luckily the iPhone was only in month 20 of its 24-month AppleCare contract.
Your humble blogger has the Apple triad--MacBook, iPad, and iPhone--and a hardware problem on at least one of them crops up every year or two.
I always buy AppleCare on all three, which is still cheaper than replacing one device when it breaks down.
Gamble if the odds are at least close to even, but not buying AppleCare is almost a sure loser.