First of all: the option “invite me to multi day games” allow you to chose if you want or not multi day games, but what about real-time ones?
Clicking the Play Now button gets you a real-time game. One click = one RT game.
This is somehow nice, but how do I stop it? What if I go for 2 weeks on holiday and I don’t want to start any new QM?
Uncheck the box you mention. Simple as that.
In my opinion the QM button should allow to set the type of game you want, the templates you are available to play and then have a button saying “Start a new game now”.
That's exactly how it works for real-time games.
For multi-day games, allowing games on demand would have a lot of disadvantages over the current system. For one thing, there's a lot of logic that goes into the algorithm to decide who to pair you against. It tries to match you against players to give you an opponent of comparable skill.
If we were to match multi-day games on demand, you're taking away a lot of the flexibility of that algorithm as now it can only match against other players who are eligible for a game at that instant. Even giving the system a 5-10 minute window adds a ton of flexibility and results in better matches.
Further, given that it's common for people to play multiple multi-day games at a time, we certainly don't want to force people to return to the page to manually click to get a new multi-day game all the time if they're cycling through games quickly. That would be cumbersome. So even if such a feature existed, we would still want to allow the "x games at a time" feature. Therefore, given that it's needed anyway, I'm not sure how beneficial the MD-game-on-demand would really be. It would only shave a few minutes off the invite time, and given that you can only play one turn right away anyway, it's not going to speed games up much at all.