There is an actual reason to heat the whole space. But it depends on a number of factors including the size of the space heater, interior wall insulation, and external temp. If the exterior was -20F then using a single room space heater would not work and might be more expensive than bringing the whole floor to 58F in the long run.
The gist is your home has a thermal envelope. When you’re only heating that one room, without insulation, the heat is evacuating to neighboring rooms. So you’re still heating everything just poorly.
On top of that, a well insulated home drops heat slower than it take to heat up. If the home is built correctly all the heaters would work in tandem to bring the base temp up to a set point then shut off and allow it to slowly drop.
But again. There’s a ton of factors here (heater size and type are huge).
Check out Hugo. Takes a little to setup but it’s completely free. You can host for free using your GitHub and a provider, plenty of tutorials on how to do it (blanking on the providers name atm)