They might have a problem with her now, I don't know. But BoJo won an election. The MPs forced him out. MPs rallied around Sunak, but the final round went to the Conservative membership, and they voted heavily for Truss. Now the MPs are forcing her out. BoJo has ruled himself out, so it's basically a two-horse race between Sunak, whom the MPs want, and Mordaunt, who finished 3rd last time, and is likely to gather the anti-Sunak vote that otherwise would go to someone like Truss or BoJo.
If there's a vote. I'm not 100% clear on the procedure this time around - the 1922 Committee which sets the rules for Conservative party leadership can pretty much write them as they go - but if the MPs send Sunak as an overwhelming favorite against Mordaunt to the membership at large, there's a very real chance that the party will select Mordaunt, and she'll step right into the same place Truss did: trying to lead a mutinous group of MPs that don't really want her there.
To underline my original point in starting this thread, I have personally argued several times on this forum that the parliamentary system is superior to the presidential one for numerous reasons. The chaos currently happening in the Conservative party is the counterargument to what I've said in the past.