That is the prudent plan if the coach and GM were not on the hot-seat. The conventional wisdom for Chicago is, "We are a QB away and need to get one so we do not squander the opportunities that the rest of the roster gives us." They have a stout - but aging - defense. This motivates overpaying for a known quantity vs. building for the future.
The top QBs in this class are Lawrence, Wilson, Fields, Jones, and Lance, as they all received first round grades. It's possible one of them gets to 20 (maybe Jones or Lance).
The NFL is a QB league. All winning teams have good QBs. Few losing teams have "good QBs." (and, yes, I recognize that a strong OL/RB roster can help). That Chicago made the playoffs (8-8, yes) with Trubisky and Foles indicates they have a good roster.
And if you are going to trade for a QB, you try trade for a winner - or one who has definitely shown flashes of brilliance. Wentz won in Philly but dropped of precipitously this year. The OL stunk and Philly lacked playmakers. Could he be salvaged in Chicago? Absolutely. 2020 was by far his worst season as a pro. INT rate was 2x average; sack rate was 2x his average. If that was anomalous, he's worth trying again. But I am not sure he's worth the king's ransom needed to get him. I consider taking on his contract as part of that ransom. If he does not pan out, you've taken on a 3-4 year contractual millstone.
On paper, making a run for Darnold makes sense, esp. if you can get him for #20 and a 4th. Why not try? You might just be getting another Trubisky. Yes, Gase was a shitty coach and Darnold shows flashes of being a top-16 QB. He shows more flashes of being a bottom-quarter QB. This is a good summary: https://jetsxfactor.com/2021/02/06/sam-darnold-concerning-weaknesses-featured-in-2020-film/
All that to say: The Bears are kinda screwed. They do not have a clear way out of being a 7 to 9 win team in the next 2 years. That is compounded by the fact that the GM/HC are on the hotseat.
BTW - the Colts are in a similar bind. Rivers retired. They have Brissett and Jacob Eason on their roster, but neither of those will get you out of Round 1 of the playoffs. But Rivers did not either