Doesnt have anything to do with being a mobile QB, in fact I would argue you'll see more sacks with mobile qbs. Brady has never been a mobile QB, but he gets the ball out quick, feels pressure and moves in the pocket better than almost anyone.
Last year Brady had over 700 attempts and was only sacked 22 times. For comparison, Murray had 31 in 481 attempts, Lamar Jackson 38 sacks in 382 attempts. Justin Fields 36 sacks in just 159 attempts. Joe Burrow 51 sacks on 520 attempts.
Granted all these Oline and overall offense situations are vastly different but the guys who were sacked the most are some of the most mobile QBs in the league, and their biggest strengths are extending plays. Burrow was probably more so the number of long developing plays Cincinnati called, but Murray/Jackson/Fields are about as mobile of QBs as you can get and some of the most frequently sacked guys in the league.
It's just a matter of taking the bad with the good. These guys can all create big plays out of nothing, but the more time your oline needs to block the more important that pass block win rate is. Cooper Rush basically drove the bus for weeks by making a read and getting the ball out quick. When he struggled against Philly was when he got rattled and seemed a little more gun shy. In theory your oline could lose 100% of the time, but if your QB gets the ball out in 3 seconds or less every drop back he may never get sacked. Also your QB could get sacked every play, but if they take 4-5 seconds to get rid of the football your oline could technically have a 100% win rate.