Let's take the pessimistic estimates of Falcon 9 Heavy, which are about $3000/kg to LEO. (The optimistic estimates put it closer to $1500.)
You are suggesting that pessimistically, Starship is aiming at $30-60/kg to LEO. (Or, using the optimistic estimates, $15-$30/kg to LEO).
I don't think in even Elon Musk's wildly optimistic press conferences he pushed a number below ~$100/kg to LEO. I don't know where you get the idea that launch costs are going to come down 50-100x.
Back-of-the-envelope calculations look like this: fully reusable Starship's flight costs roughly the cost of fuel, which is 1-2 million dollars per flight, both stages. If the Starship carries 150 tons to orbit per flight, and it costs $1.5e6, then we have the price of 1 kg on orbit equal to $1.5e6 / 150e3 = $10. Which is rather comfortably 100 times cheaper than SOTA.
Wildly optimistic would seem to be even lower estimations. If both oxygen and methane we can get from atmosphere - and we have both efficient detanders and demonstrations of e.g. Terraform Industries which use solar panels and oxygen to pull CO2 from atmosphere and produce CH4 - then the question is of optimization, and we're just starting here for this application. So, a flight of Starship might get cheaper than $1 million - the question is, how much and how soon?
I haven't seen anywhere suggesting a $1-2m launch cost is a reasonable target. Sure, maybe $10m is achievable, but $1m is so far off it's not useful as a cost estimate.
Yes, because Starship promises 50-100 times cheaper delivery of kg to LEO.
Read https://caseyhandmer.wordpress.com/2021/10/28/starship-is-st... on the subject.