We have been around the block using this technique in combination with another process.
First, we found that there was no harm or losses if the queen cage is CENTERED in the hive where she remains recognized.
We started with push-in cages that were made from #8 hard wire mesh. The bees tore up the frames too much trying to release her so we now fabricate small cages.
"I'd rather remove her and let them raise a new queen than cage her, but the timing of being queenlees for that month will increase the honey harvest."
You are sure right about that! Much has been written about this by George Demuth and Killion.
We know that the workers duties can advance or retard due to circumstances.
George Demuth (former editor of Bee Culture)had a cool quote, "Are we raising bees for the harvest or ON the harvest?" Meaning that the increase of honey foraging at the peak of the flow can sometimes be much more important than raising tons of brood late in the season.
These writers had no intention of causing broodlessness as a method of rendering Varroa vunurable to attack.
If Sucrocide works for example, one could treat on day 25 and expect a clean hive. Only follow-up tests would tell.
Controlled broodless periods in combination with effective mite removal strategies can reduce the need for treatments greatly, especially for those yards somewhat isolated.
I have exactly ONE hive more than you.
That makes my opinion beyond question.