For about 15 years of umpiring, I've worn turf shoes. I did wear adult softball cleats the 1st 2 years (had them from playing and no $ to spend on equipment). They greatly contributed to big heal spurs which became very, very painful.

Wearing turf shoes with heel cups and pads and a little Aleve before games helped.
Then I found the Nike football officials shoe! Extremely comfortable from the first time I put them on and lasted 2 long seasons! I have bought them ever since. They were recommended by a man that owns a referee/umpire store that's here locally, and officiates football. They're great shoes!

Oh, and BTW, I've never worn steel toed plate shoes, ever!
No foot injuries and they're just plain uncomfortable.
I've had more injuries to my hands and fore arms than anywhere else. I use a wide stance, and hang my hands down between my legs as I was trained, but now I think when I go back to umpiring, I just might buy some padded fore arm guards!