I don't like the idea of server exclusives at all.
The reason why Version exclusives exist is that Gamefreak wanted to encourage players to trade between each other, or just plain make players buy both versions. There are other things they implemented to encourage trading, such as starters, choice Pokemons (like Fossils) and trade-evolution Pokemons. And because breeding exists, you just need to get any single Pokemon of the specie to get started on creating your perfect Pokemon if you need to.
However, here, this is a completely different situation. Trading is already a common activity between players, although in a different shape than in the original games. We still got trade evolutions, but we also got commerce type of trades, such as daycaring, selling and lending. Sure, server exclusives encourages another type of trading... But it comes with a huge bad point.
If you want to trade server exclusives, someone HAS to do a server transfer. A server transfer means that you quit the current guild you're in, and enter a community for which you may not know anyone. Some players are totally fine with this, but for players who really don't want to leave their guild, even temporarily... Their only option is to wait for someone to show up and sell the Pokemon they need, with the very stats that you want since we have no breeding or alternative feature. And because they're exclusive, chances are they'll purposedly set a higher price, making it not worth it to buy. As a player, this is NOT a situation I want to be in. It's just frustration.
As for the other possible reason of version exclusives, being making more money... Well, as far as I know, we still have a good enough income to pay for the servers, no? We have plenty of things to sell in the cash shop, many players buy coin capsules to resell them ingame for money, it's looking pretty healthy to me. And besides, if that's the only reason, you're just going to make the playerbase more angry and distrustful than it already is.
There's other consequences to this feature, which is unrelated to reasons why you'd want this in... If we implement server exclusives, it will become more complicated to do new modifications to our server. Server merges means we have to get rid of the feature at the same time. Adding a new server means we need to split more exclusives.
And finally, it makes the server choice more annoying for the players as well. Will the exclusives be displayed before you even select a server? If they're shown, it's kinda too much information when you're just starting out (and could also scare players away because they don't like that feature). If they're not shown, you're making an uninformed choice and may regret your choice of server. And regardless of these, if you're joining a group of friend, but they're on a server where your version exclusive does not spawn... That already takes a big hit at your motivation to even start the game.
So please, don't implement this. There's too many bad consequences, and its only purposes are already fulfilled by other features.
As for time differences... I don't really mind, server times are already completely out of sync with real time, and it doesn't change availability... Although it could encourage players to create alts for hunting in succession in both servers. Since we want to discourage alts, I don't think that would be a good feature. That said, if you do implement it, just make sure that you don't break time-based quests in doing so.