Well, they’re doing it. There were some early NFT-based games (that seem to be collapsing already, as they are basically ponzi schemes), where to play the game you have to make a significant investment in it (like $1000 worth), and then “playing” the game generates NFTs which can be sold for income.
For traditional game publishers who have already had real-money transactions in their games for years and that are only more recently getting on the NFT-train, NFTs might be appealing because of their unregulated nature right now. They might be seeing it as a way of avoiding some of the issues they (or other publishers) have had with game item marketplaces. (The NFTs don’t really change anything, of course - the regulatory issues would still be there, and the in-game assets are only ever going to be useful for just that game, even if they sometimes imply otherwise.) So far the game companies (e.g. Ubisoft) doing this are partnering with third parties to run some of the crypto stuff and the marketplaces, but if they’re serious they’ll eventually run marketplaces themselves.