Yes, high fever is dangerous and why monitoring is important and hospitalization is required if the fever goes up. A thermostat is a (I am pretty sure) a recommended tool for parents to own and use during an infection. If the fever do go up there is common available medicine.

For covid it is good to keeping an eye on oxygen levels. There are not many good tools to do this, through the skin do turn blue when things start to go very bad. Oxygen capacity can go down a fair amount before there is obvious signs, especially if the patient is laying down. The recommended medicine is pure oxygen which will require a hospital visit.

Personally I am more worried about covid. It is easier to monitor the fever of the flu, the signs for trouble is more clear, and the medical guidelines for when to go to the hospital is well established. Worrying oxygen levels are silent, harder to measure, and the medicine isn't something that people usually have at home. The guidelines are not fully established and there is ongoing research studies on the effects.