In this enviroment, what if anything would be the negative effect of opening 10-12 different accounts (with Regional/local banks) if they all run checksystems?

In any environment, I wouldn't suggest opening more than two accounts every 90 days if they're going to inquire into Chexsystems. You probably won't have problems with three accounts in that period, but stay with two to be safe. Banks can get nervous about this. You even risk recently opened accounts being closed on you if they see you opened more accounts afterward. That, along with the fact that there is probably no valid reason to open so many accounts at once, aside from some inner-need to collect bank accounts.