The manager you're thinking of is Connie Mack, who guided the Athletics for an amazing 50 years. He wore a business suit and straw hat. You're right, it's traditional for the manager to suit up in baseball duds. No other reason. The chances of Larry Dierker taking the field as a pinch runner are zero.
Spikes are completely unnecessary.
I think managers should wear something more comfortable, like penny loafers or fuzzy bunny slippers. You have a vocabulary.