There is no doubt that Nogowski is a superior defender at first. That isn’t enough to overcome the other obstacles, however.
They really like Miller, who has 75 MLB games at first. They want more at-bats for Edman and moving Carp to first would be so obvious. The defensive upgrade at third would offset some of the loss of Goldy at first. Either of those (and probably other options cited) would happen long before Nogowski would get a chance.
They have many outfield candidates to soak up DH at-bats not even counting Carlson on the horizon.
The biggest problem with the 2020 Cardinals will be scoring runs, same as in 2019 and 2018, for that matter. Remember that this is a team that (pre-Goldy) played Jose Martinez regularly at first because they needed the offense so badly. If Goldy is injured, they aren’t going to replace his bat with Nogowski. It just won’t happen, especially not in a 60-game sprint season.