In most PoS designs, registering a new validator account takes some fixed amount of time, just as a measure to prevent grinding attacks. If registration takes an hour, and I can't predict the random seed an hour in advance, then I can't predict how my account will be scored, so grinding would be futile.

Most PoS designs don't otherwise favor old accounts. I know Peercoin does, but that's a very small project, and I'm not aware of any others. Ethereum 2.0 definitely won't have any such mechanism. In the current spec [1], staking is binary; either you have an active validator account or you don't.

[1] https://github.com/ethereum/eth2.0-specs/blob/master/specs/c...