El Cid: I probably would not know exactly how many games I would get (for instance on a 21 points match with doubling cube)
That would be a single game.

Note that for round robin tournaments, you don't know exactly how many games you get now-a-days either - it will depend on the number of people that are in your section. For elimination tournaments, you will know exactly how many games you get. If it's a 3-game match, you will get 3 games. Not 2. Not 4.

I would end up (at least on what concerns to my plays only) slowing up the games.
Your games might become slower, but your matches will be faster. And the tournament itself as well.

Note also that if we have a tournament "2 games for each 2 players", the games are now already played in parallel.