There are a couple of issues with this proposal.
1) There are some errors you can easily fix (and in fact have to fix or the game will continue to have short increments giving you the same error every time), or have known workarounds. There is no way for the game to know which errors you can easily fix and therefore only show those
2) Some errors, especially data access ones, result in an endless series of error 91s (Microsoft error codes). With no popups, the game will simply hang for no apparent reason.
Obviously the ideal is to have no popup errors. My current campaign has had only one so far, connected with the Check All Pops option, which is now fixed If you do have errors though, read the message and report them so I can fix them for the next version.