... But if "cost wasn't a factor" then we could just simply dedicate the electrical output of fusion plants to brute-force CO2 out of the air.
But there are other environmental impacts. Fusion, even compared to fission, has an extremely small footprint (per megawatt). Its fuel is easily available (isotopes of hydrogen). It does require some pretty advanced magnets though, so it will contribute to the strip mining that we do for rare earth materials (though this applies to all energy forms, including solar and wind). I don't have numbers to say if a fusion reactor would use less total rare earth metals per megawatt compared to something like solar or wind.
One thing to note though. Once we get sustainable fusion reactors, it will still take a bit for that cost to come down significantly. That usually takes 10-20 years. This is a pretty common pattern. We've seen it from the price of laptops and cellphones to the price of solar panels.
But with fusion the endless claims of "too cheap to meter" are because how much energy there is in a fusion reaction. [0] We know that fission produces a lot of energy (but is expensive) but fusion produces significantly more. It also doesn't have the radiation drawbacks and so it is expected to follow the S curve (fission did initially but things changed. This is part of why France has so much nuclear).
So if (big if) fusion does follow this S curve (which there are good reasons to expect it to) then it could provide a very cheap and sustainable energy source. Yes, it is a bet, but every technology is. We won't know until we spend significant time and money into researching it. But honestly, a few billion dollars isn't that crazy for the potential upsides. We've spent that money on far greater risks with lower payout. Despite what the OP said, the money for ITER does not require international collaboration. Any rich country could do it themselves.
[0] (Fission and fusion can yield energy graph) http://hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin.htm...