Except they'll have less time between other matches, so there'll be more FATIGUE then to make up for it.
The only way to genuinely reduce this FATIGUE is to reduce the number of matches, and there's no football authority willing to do that as it would reduce their own power and importance.
You don't seem to get the concept that you can do more once you've had a break. Have you never been running, got tired and slowed down, stopped for a bit and, when you started up again, you got up to a higher pace and being full sure that you'd absolutely ran much further than you would have if you had not had the break? The idea that you need to reduce the number of matches to reduce fatigue is complete nonsense.
The corollary of every break is increased productivity after it so I'm not sure why it's so difficult for so many people to grasp this.
Just look at the productivity of children in school before and after break or before and after the extended lunch. Teachers aren't being nice by giving time off: they know they'll get more more of the children with breaks. A lot of people might say children should be obedient and pay attention but at a certain point you have to accept what children can do. This is the same with professional footballers: people can talk about how much money they earn but you have to look at what's best for them.
People within football want to ask how can they get the best out of footballers and the fans just want the footballers to work, work, work and seem to care more about effort of the players than about them actually working in a useful way.