What will happen after these 5 games? Now, the stronger players will play against the weaker ones, and then what? It turns out that one player will play, say, 10 games, and another will play 6, and how will all of this be tracked? There are currently 24 players, and there have been even more in the past, so what happens then? Playoffs? And how do you create pairings, and so on? Don't interfere with the rules of existing tournaments; they have been held many times, and everyone is happy with them. If there is a fear of facing unfairness, just play fun matches and have a season!
Those who could/managed to play 5 games within the timeframe did so, and a table of points/Berger's coefficient was created. The top 20 made it through, while the rest did not. This is the same as it is now in terms of results, but completely different in terms of organization.
Moreover, if I win three games, I will most likely advance from the first stage and can skip the remaining two games.
At the very least, this option makes it easier to find an opponent, because you are not looking among the 5 available, but among all 20, and if you can't meet the deadline, the reason is most likely you.