I really like the idea of them being able to say "don't worry, you can't get overly addicted because we only offer one a day and don't let you binge." And as owners of the IP, they do have that right.
I used the wordle archive so that I could go back to days I missed. That way I can still share the experience with my family even if I've had a really busy day. It's undeniably a positive and I'm upset that I can't do this anymore.
Several of the variants e.g. Quordle have an unlimited play variant, but I've never felt a desire to use it.
And people might start going to the archive instead of the main site, seeing as it has a major features the main site doesn't. (i.e. ability to keep playing) Obviously they don't want that. They want 100% of your concentration to be on today's word. They want you to look forward to tomorrows puzzle where you can play again. Playing archived games decreases that, as you can satisfy your craving that way.
I sort of miss the archive, but at the same time I am glad it is gone. I like that feeling of "I'm done with Wordle for today" without that nagging "but I can do 100 more .... now where did my morning go?"
This is a rare case where I support a company being protective of its IP.
All I can say is that this is not my experience. In my family WhatsApp people post today's result and we sometimes have a bit of a chat about what it was like. Sometimes we do today's globle and quordle too. The quordle has an infinite play version but I don't think any of us spend much time on it.
I think their motivations are a little bit less altruistic. Which your post helped me figure out. They don’t want an archive because that requires everyone to visit their site at least once a day.
If there is an archive people could skip a day without repercussions.