In the old pre-internet days people would often have to pay for chess books to read during correspondence games. I doubt there were all that many people who played them who complained that their richer opponent had an unfair advantage through being able to buy more chess books to help them with their game.
An occasional auto-vacation mode would only allow a player to play any better if they were actually using all that time studying their positions. Maybe there are a tiny handful of players on the site so dedicated to winning by unfair means as to do that, but for the vast majority the only direct effect it has on the game is that an opponent doesn't time out. Personally I don't want my opponent to time out of a Daily game any more than I want to myself. Winning on time is for live Blitz/Bullet games.
People who pay to support a site (whether it is voluntary or not) obviously expect to get something in return though, and among the various perks that paid membership gives auto-vacation is just a minor add-on that is 'nice to have'. And I very much doubt that the money from paid memberships is spent only on adding or expanding features that only paid members have access to.
As far as the amount of vacation mode is concerned, certainly I have no defense of that. Anything above 30 days is totally unnecessary, paid or not.
I wouldn't include training of any sort as "directly affecting" a game in the sense that I intend. Obviously it affects the game, but not during the game. It's an external element of preparation, not a mechanic of play. I thought the opening explorer was odd when I first learned about it as well, but it makes some sense. You may be reading a chess book during a correspondence game and come across something that benefits you. There's nothing really wrong with seeking out information that is particularly relevant to your current position, provided that both players have agreed to it. Of course, on chess.com, for many players, that agreement is made simply by playing a daily game on the site.