In POW the second you receive a block you rush to work on top of it as you are more likely than to be picked to create the next one. Why are people in POS incentivized to attest instead of waiting for others to attest? Is it just that at the last possible

I generally like POS but I realized that I don't know how that works. In POW when you see a block it's your best guess what to build on and you want to start immediately. So your revenue is increasing in how early you start to build on the next one. That does not seem the case in POS. It rather seems to be the opposite, it is risky to attest as quickly as possible because you really don't want to attest the wrong block. Can be that I misunderstand something of course. Why is not everyone waiting on all others? My thoughts are not perfectly clear but it feels like this could have security implications.