We're well into the realm of arguing ridiculous scenarios, but in that vein: the Earth will 100% become thermally uninhabitable before Mars as the Sun turns towards being a red giant. There will be a period of time when a terraformed Mars would be more temperate than the Earth.

A desire to explore and settle a new frontier isn't legitime?

Not so much. Populations look for new better frontiers, not merely new frontiers...

Desire is reasonable. Yet permanently settling Mars or beyond is unreasonable based on some fundamental physics.

Which laws of physics prevent a permanent base on Mars?

Gravity primarily and the lack of carbon on the surface. Also the lack of a magnetic field to maintain atmosphere and shield from radiation.

Gravity can be solved the same way as on a space station (spinning), you just don't put the floors at the same angle because you're adding the constant vector from the mass to the frame of reference vector from being in a centrifuge.

Artificial magnetic fields are easy. Sometimes we do them when we don't want them.

Carbon is 1/3rd of the atmosphere (such as it is) by mass. Conveniently in solid form near the poles during Martian winter.

I'm not sure it has nitrogen in any significant quantities, though…

Spinning enough to produce usable gravity is non-trivial and building something like that in space requires overcoming Earth's own gravity well.

Non-trivial yes; although house-sized spinning fairground rides are a thing so it's clearly infinitely easier than the gravity of Mars being a law of physics.

And the only sane way to do this is ISRU, so we don't need to overcome Earth's gravity well for the structural mass.

Mars has carbon in its atmosphere. I don't think we have the necessary data to say that Mars' lower gravity prevents long-term settlement. Mars has enough mass to keep an atmosphere for millions of years, but you probably want to mostly live underground for the foreseeable future.

, which is a great reason.