Copyright and patent law aren't relevant to this discussion. We're talking about goods that are purchased and then later rendered unusable by the seller.

I disagree. We're talking about goods purchased, and separately services without a paid support contract, and this is all about copyright law.

There's nothing illegal about selling a game where the servers only work for a week, if you say the servers are only going to work for a week unless you pay more.

The question is, what's reasonable if you don't say anything at all? Forever? A year? Five years? And that's not a trivial question.

If copyright law lasted two years, there would be nothing stopping someone from reverse engineering the service under one of these games after two years and running it themselves (barring serious cryptographic blockers).

Furthermore, the developer would have planned for that expiry of their IP protection. There's a loss to the game studio if they give away their intellectual property while it is still protected.

The only reason this is difficult at all is because of copyright law, and I suspect patent law as well but I think that's murkier.

If you start looking at this through that structure, I think it will make a lot more sense to you why each entity involved takes the actions they do.