^ Also coincided with the 2 starting tackles being out (starting left guard was already out for the season), not to mention this was before the Saints got a somewhat reliable kicker in Maher (one can say their kicking woes cost them 2 games).
The Saints D also didnt play nearly as well as they did during the last 4-5 weeks of the season and there was that horrible call that took away the EZ INT in the Titans game.
Siemian being a pocket QB, when the Saints (already lacking in weapons) lost Kamara and then Troutman (their starting TE who is meh) and both their starting tackles, Hill was the better choice at QB since he could generate some O with his legs.
Horrible luck for TS, but the more astute observor (not to mention GMs) will pretty much ignore the 0-4 record as a Saints starter.
Didn't Taysom Hill already pass him on the depth chart?
Hill was #2 from the get go (once Winston won the job in training camp), but Siemian was still learning the playbook (having run the scout team when he joined the Saints midseason the year before).
While all the talk was about the QB battle btwn Winston and Hill, Payton would always try to bring up Trevor.
While Hill is one of Payton's favorites, Sean is going to do what's best for his team, and while Winston won the job out of camp, never got the sense that Payton was really comfortable with Jameis.
Despite spending less time in the Saints system, Trevor could run more of the playbook than either Winston or Hill.
Hill's injury may have changes things, but wouldn't have been surprised if the Saints didn't resign Winston during the off-season with a QB battle btwn Trevor and Hill.
An interesting tidbit is that the Browns were one of the teams interested in trading for Siemian during the season (kind of odd since they already had a pretty good backup in Keenum, but maybe they were concerned about Mayfield being able to see the field again).
One thing that Trevor needs to improve upon is making more off schedule plays (even when he had the opportunity to scramble/run, more often than not, he didn't), but then again, that increases the chance of injury as we saw with Winston and Hill, not to mention Trevor during his short stint with the Jets.
So maybe it's best for him to just do the Brady/Manning thing and stay in the pocket (and self-sack if need be).