It's got to be largely through necessity, surely?
To find players to improve even a mid table premier league team is very difficult because there are so few players who are both good enough and in budget.
Anyone good enough will be on the radar of at least one or two of the bigger clubs, which means the player will wait for the bigger clubs to decide before they entertain the likes of us, even if they have only an outside chance of joining a big club. Even if we bid early in the window, the better players will probably want to wait and explore all their options.
Plus, I think not leaving the selling club and player too much time to think is probably deliberate. It's a very old strategy but people like Warnock used to swear by the practice of making a bid late on deadline day to ramp up the pressure on the seller and player, who have to either accept the offer or accept that there may well not be a sale, as there isn't time to make alternative arrangements. I was told all about it once over breakfast by none other than a Mr D Freedman Esq no less, who at that time was coaching the reserves at Palace and doing a sort of apprenticeship under Warnock. But that's another story...
Things have moved on a bit, of course, but I'd still think that Parish making an early bid for a player gives the selling club and agent time to create an auction to the benefit of both but the downfall of palace.
Of course, Parish could make early offers that are too good to refuse and get the players in early, but in an open market that generally means paying more than anyone else is willing to. We can't do that very often before the budget is blown on too few players.
Ultimately, the proof that Palace aren't acting unusually is found in all the other clubs doing loads of deals in the closing stages of the window. Everton have brought in three today I think so far, when presumably they knew all summer that they wanted players in those positions. Everyone is at it.