But, all players should have the same amount of time to make their moves, regardless of how much they pay to play here.
I totally disagree, paying Members do so for additional features/perks and this includes vacation time.
In particular, the Premium membership benefit of having Time-out Protection for Daily Games is the main reason I subscribe to this Site.
A commercial website needs to be run as a business, not on the basis of some lofty ideal of "fairness".
The idea of making a drastic change to the way vacation time is accrued, such as using ICCF rules (30 days for 10 moves, +vacation time) or Go rules, as has been suggested, is appealing, but it would involve changing how the time on the games are shown for all players. It would also entail educating all these players on how to use the system.
While the benefits of using postal time controls for postal chess are real, the costs and the complaints that will ensue as a result of such a drastic change make these unappealing for a large site that already has a cc system in place.
I still think the best practical option for the site is to reduce the maximum amount of vacation time to 30 days per year (rolling), and make the vacation time the same for all players regardless of premium status.
I also agree with @MGleason's point that new players (less than 3-6 months on the site) should have less vacation time because there are so many accounts that start a game, then abandon it right from the beginning. If a player is allotted one week's vacation time until they've been on the site for 3 months, then 2 weeks until they've been on the site 6 months, then the full 30 days, it would resolve most of the issues.
The vast majority of members here are amateurs (which means they play for the love of the game). Most players have no experience of serious chess, either over the board or in correspondence. Many players don't seem to understand that cc chess is meant to last for several months or even years! They want their games to be over quickly, and accept the site's time controls as they are. They just want their opponents to play quickly too, especially when they are losing. It would be a mistake to make fundamental changes to the site's cc (online) time controls.
But, all players should have the same amount of time to make their moves, regardless of how much they pay to play here.