2nd, SS and 3rd the pocket is too deep with C or 1st basemens mitt. Everything being equal the infielder is going to start their throw to 1st quicker with a 'normal' glove.
OF or 1st a C mitt would be OK. Softball catcher mitts are nothing like baseball catcher mitts,
I thought that in most rule sets, a "mitt" could only be used by a catcher or at first base.