Are there any restrictions on who should have to "punch in" if the bank switches to an automated time card system? Specifically... are exempt employees prohibited from punching in?

Describe "exempted" employees in your organization. The only people who use the timeclock (it has the Simplex logo) in my organization are hourly operations center employees. Employees who have an annual salary and for the most part are analyst/specialist/consultant titled or who are officer-level employees do not "punch" a clock. I guess these latter people would be "exempted".

Normally, exempt employees are paid a salary, which covers all time for the year. You couldn't pay them overtime for 50 hours nor deduct pay for working 30, all it would be is a gatekeeper.

While there may be no legal rstrictions, it may provide negative morale.

Be very cautious if you are thinking of having Exempt staff punch a time clock. Sometimes the Exempt/Non-exempt lines are a little blurry and you could run into FLSA problems and end up with a law suit on your hands and liability for "exempt" overtime pay.