The launch facility they have in Boca Chica is surrounded by wildlife preserves, where are they going to put a solar farm big enough for a usable methane plant?
To put it in perspective, a square meter of solar panel puts out about 200 watts.
At atmospheric pressure, a cubic meter of methane gas contains about 40 million joules of energy.
40 million/200 = 200,000 square meters of solar panels needed to produce a cubic meter of methane.
And that’s assuming the process is 100% efficient. It’s also not counting the energy needed for the pumps to pressurize plant, or the methods they would use to extract or move the carbon dioxide, or cool down the methane.
That 40million joule figure is for gaseous methane, starship needs liquid methane to run, so the methane would need to be cooled with industrial refrigeration to turn it into fuel, which adds even more energy to the equation.
For the amount of fuel Starship needs, the Sabatier process is not feasible if you’re doing it with solar panels and planning on launching more than once a year or so. Not unless they want to pave over a small city with solar panels.
Putting energy back into CO2 to get fuel is not really economically feasible. It’s a useful process for mars for example, because you can drop off the plant and have it trickle fuel into a launch vehicle while you build the base and wait for the crew to arrive.