It's not an idea Valve is interested in. This has been stated explicitly. Valve might not be able to throw the money around Microsoft is to get games on Game Pass. Company A doing something may not create a need for company B to copy them and try to beat Company A.

But who knows what happens tomorrow. Positions change and evolve. But I wouldn't hold my breath at this point.

I think Xbox Game Pass pricing development shows reasons to NOT do it.

So, why do Microsoft and EA do that and Steam doesn't?

It's worthwhile for EA because they are their own publisher and therefore have no third-party developed titles in their subscription model. Therefore their only costs are of opportunistic nature. They take the whole monthly cake for themselves.

Contrary to EA, Microsoft does sell third-party titles on the XBox and Microsoft store and therefore, their subscription model is more of a loss leader to encourage players to buy the games they loved to play on their store. They have to share the subscription profits either by agreement or usage ratio, netting them not only opportunity costs in lost sales (if the sub time covered the whole gameplay from start to finish), but also spendings on deals.

Steam doesn't need a loss leader to attract customers (it's by far the most popular PC games storefront) nor can Valve profit from rental agreements with several thousands of publishers as those aren't Valve's games to be rented away to begin with.

for $20 a month you can buy multiple games and build a backlog.
A much better system where your games don't disapear when some backroom deal goes wrong.