Employer (bank) restricting the use of other brokers

As far as I know, it is not. The FINMA states in “Circular 2013/8 Market conduct rules”

There is no requirement for custody. Especially, since the board is often exempt from the made up custody requirements (because they would bolt rather than suffer such rules).

Also compare for the conflict of such internal regulations with Art. 323b Abs. 3 OR also known as “Truckverbot” (ban on truck systems) which voids agreements that use salaries to the benefit of the employer. See my post: