This is a very well known bug of 2020 and every user experiences it. Asobo say it on their desk, so sooner or later it will be fixed.
What makes me wonder is that so many of them claim to be at least PPL holder pilots and I just start doubting that claim if they weren't able to recognize that even the simplest prop plane is almost uncontrollable due to the sensitive controls.
There's a workaround in FSUIPC though (by increasing the range of the variable) and it works fairly well.
At present the flight model of FS2020 is unfinished.Oh well, I'm sure Lapi in the end will manage to provide a proper B738 model to all of us.
The most important tables do not work in "modern" mode and Asobo say they do in the work "legacy" mode, the problem is that they don't work there either.
"Modern" in this regard means they take out of our hands the most important tables that determine an airliner.
They have promised to change this, so the future could be very bright because the new dynamic engine is quite good and innovative, but as I said above" MSFS is an unfinished product, so it will definitely take time to come to a solid level.
The same happened to FSX when only "Acceleration" provided the necessary dynamic changes.
I have both the 738 and the A320 flying here - as well as the engine allows it at present. It is a different question though if the suite itself will provide the needed support in the near future.