Few things in major league baseball are more puzzling than watching a professional dive into first base. It’s never faster. Not the way I’ve ever seen anyone do it. Even if you execute the perfect dive and get there 10 milliseconds faster, it’s not worth the risk of injury.
Regarding plays at the plate, I would point out that home plate is not a soft bag like 1st, 2nd and 3rd base. They’re not exactly soft bags, either, but they do have enough give so that when you plant your metal cleated foot on them at full speed, you’re probably not going to slip and fall.