Nah, that's peak. Not only would that reduce its prestige, but would unnecessarily increase the football schedule
Now that it's the half, I'll come back and respond to these good points:
1. First, I don't think it would reduce its prestige. Champions League happens every year, but winning that still has extremely high prestige. The level of play/talent is what creates prestige to me. I think expanding to 48 teams is really going to hurt prestige as trash teams like, say, Vanuatu or the United States

start getting into the tourney and dragging down the quality of play (though you might well agree and think that it should stay at 32 teams every four years; I'm just speaking to what I think determines "prestige" of a competition)
2. Second, the point about the football schedule is probably the strongest one, and in truth, I don't know if doing it every three years would be too much. I just am too ignorant of all the different cups and how that might change schedules. Adding a bunch of qualifying games to the schedule really might hurt player fitness. You could be right about that one.