Except the game is played by millions and will inevitably be played by many fewer in this scenario. People can trivially make clones but it won't be the same as part of the fun is that it's the same word for everyone, and I assume copying the day's word would be even more legally dubious than copying the gameplay.
So in that scenario, I don't think "everyone wins". A free, universal bit of fun will have become a paid, niche thing for NYT subscribers. The vast majority of (continuing and former) players will have lost something.
I don't at all begrudge the developer taking the opportunity to cash in, but if this is what the NYT do I certainly will resent their part in it. It's a bit of mild fun that doesn't need to be "monetised".
The crossword comparison is a bad one, btw. The setting of each crossword is a separate skilled, creative act. Not many people can do it, and those that do deserve to be paid for it. There is practically zero daily effort in running Wordle, just static hosting and choosing a word each day.