Ok so we have Early Access right now.
In theory early access is a bonus for people who buy the game early because they can experience the game as it is being developed, they can also essentially alpha-beta test the game and often have an impact on development as well.
A lot of the time though Early Access is either an attempt by developers to get people to buy an unfinished game... OR a defense mechanism because they believe that Early Access is unreviewable as "Hey, we are in early access! don't judge us" (There are even finished games that stay in Early Access for just this reason).
-I laugh that the whole "You can't review Early Access" has entirely blew up in people's faces as yes... the gaming world caught on... forcing people to actually HAVE to review Early Access games. Ha ha ha!
Yet I am not talking about either of those situations I am talking about the "Eternal Beta" or "Eternal Early Access" games. Games without a real intended stopping point that want to update the game continuously, along with the freedom to do so, without ever really reaching a finished point (or at least until they get bored).
Yet these still go by Early Access which implies a end point. Your not having "Early Access" because by all intents and purposes the game has no end and thus you are no more "Early" then anything else (One cannot be early for an appointment that has to set time).
Mind you this ultimately won't work because they don't want the Early Access stamp for accuracy. So even if they did have a new title like "Flexible Development" or something like that. They wouldn't use it. In fact I'd go as far as say most eternal Betas wouldn't even admit they are eternal betas.
Should we have a new system for Eternal EA games?
---
Personally and I know how people will disagree with me... but I don't like Eternal Beta games. They are a lousy excuse...
"Ohh but they are always changing the game!" Who ever said you couldn't add on and change a finished game?
Eternal Beta games often just end up broken messes that are missing vital features... And they will never EVER add those vital features because those are hard work.
It is kind of the thing about Eternal Betas... They are eternal because they add fluff and superfluous systems, while the required core gameplay rots.