I don’t think it’s a good idea. You body needs energy to defend itself.
Discussion
The saying goes:
Starve a fever, feed a cold.
That’s worked for me but I don’t get sick often. Was a little sick yesterday and fasted all day and had a huge dinner. Woke up feeling fine today. No fever though.
When someone is sick appetite goes down anyway. So generally you are not eating much.
But soup works as one needs plenty of fluids and vitamins.
For me, if I have a fever I don’t reduce it. I let my body fight. Unless it’s very high fever. Colds, I almost don’t care lol.
But like you, I don’t get sick often, maybe one every two years.