(for the day or two it takes to do a clean extermination)

A thorough extermination actually takes months between two extensive treatments to make sure all the eggs (which are staggeringly resilient) were caught between both treatments.

If it were that easy, this would have been solved everywhere already. A day or two is almost certainly not enough, you also have to do adjacent apartments (whose inhabitants probably aren't going to be very happy, especially if they have to leave for the fifth time), your map can show that it affects like every other building (especially when it's a large apartment block), the temporary housing is at risk of becoming infested too, which will make people fear being there, etc.

It actually sounds a lot like zero covid - simple on paper, you try it, you find out it doesn't really work, and then you're left with the choice to either change strategy or try to go harder and cram it through regardless.

Either that, or they would weld the people inside of their own apartments while they raise the temperature to 118° for 90 minutes.

Problem solved! Congratulations citizen, plus five to your social media score. You're now allowed to buy hot dogs from 7-Eleven.