Josh Allen was drafted 7th in the 2018 draft; Buffalo traded up from #12 (with TB) to select him; Dallas drafted #19 that season (LVE)
Patrick Mahomes was drafted 10th in the 2017 draft; KC traded up from #27 (with Buffalo) to select him; Dallas drafted #28 that season (Taco Charlton)
Aaron Rodgers was drafted 24th in the 2005 draft; Dallas drafted #11 that season (DeMarcus Ware)
So teams trade up when they see a QB they want and in the above 3 cases, 2 of the 3 teams traded up and as a result all 3 teams got QB's that took them to a Championship game or the Super Bowl.
Looking back at the Super Bowl winning QB's since the year 2000, here is a breakdown of what round the winning QB was drafted in (repeat winners such as Tom Brady count multiple times in the respective round selected):
1st round drafted: 11 (Dilfer, Roethlisberger, P. Manning, E. Manning, Rodgers, Flacco, Mahomes, Stafford)
2nd round drafted: 1 (Brees)
3rd round drafted: 2 (Wilson, Foles)
6th round drafted: 7 (Brady)
9th round drafted: 1 (Johnson)
So, of the last 22 Super Bowl winning QB's, 11 times (50%) have been by 1st round drafted QB's and 14 times (64%) by QB's selected in the first 3 rounds(Brady of course being the outlier with 7 victories as a 6th round draft pick).
While of course the likes of Brady and Johnson show it can be done, the fact of the matter is the odds of winning a Super Bowl with a QB not selected early dramatically lessens.