Obviously nothing is more relevant than it being their favourite experience that year for a game of the year thread. The point of contention is whether its original release is the only year anyone should be allowed to consider it, or if the year it was released on their platform also has relevance. They're playing the game in the context of its release for them.
Maybe they're an xbox gamer who couldn't play a title formerly on playstation only and they've been waiting for it to get released on their platform. Maybe they're an FFVII fan who only plays PC games waiting for FFVIIR to come out on the platform they use. Maybe an epic games store exclusive finally becomes playable elsewhere, and it's a hit among a bunch of gaffers who don't partake in EGS. I'm hoping darkest dungeon 2 will be really good, maybe I'll love it like I did the first game, but I won't know about that until it's not an EGS exclusive, so even if it's one of my favourite games of all time, I wouldn't be able to vote for it when its released to the wider public because that will be after its earliest release. If we change the current rules, that is.
Once you get into this mentality that only the very first release of a game can be discussed, you eventually get into the territory of remakes and remasters and arguments about why for example, a 20 year old game like Diablo 2: Resurrected is or isn't allowed. Everyone is going to have different opinions about remasters or new versions. Some will say of course this one should be allowed but not that one, this person will say some game hasn't been changed enough, someone else will say it has, everyone's feelings will differ. D2R is really the same game underneath, so its real first release was 20 years ago, someone could say. Someone else might say things like being able to auto gold pick up totally changes the game in their opinion. Someone else will say it may be the same game but it's been so long many people are getting to play it for the first time with this release, someone else will say what does that have to do with anything? Opinions about eligibility will differ endlessly, but that doesn't matter if you operate with simple criteria like we have now: was the playable content released on something this year, yes or no? You can circumvent everyone's endlessly differing feelings and opinions and just go by the calendar, something you can't do if you only count first releases because different people will have different takes on whether the changes to a "Definitive Edition" or an "Enhanced Edition" or whatever it is are really enough to consider it a new experience or not.
The consequence of strictly cutting re-releases or ports or enhanced editions or whatever out of the running, is less thread participation. Fewer people will be able to vote on the smaller list of games that are eligible... Unless they are going to guess what games they expect to like the future, when it's released on their platform. And the consequence of the system we've been using isn't that skyrim will win every year, as someone joked. That's been proven to not be the case. (Skyrim wasn't even the best game the year it won GotY btw, Dark Souls came out that year.) The consequence is a bigger drop down menu to scroll through when looking for the games you played. I think that's only a bother for a short time.