It's a mistake to assume the marginal cost scales linearly with payload. Fuel will (ish), but many other costs are fixed per launch.
I'd argue your estimate is not aggressive. SpaceX continues to claim an eventual marginal cost in the high 7 to low 8 figures per launch. I'm inclined to believe that deep analysis over a back-of-the-comment Fermi estimate.
So if a Falcon 9 costs $50M to launch, then 70% of that cost is SpaceX profit/recouping its design cost. Starship is supposed to be even more re-usable so lets assume that they only need 30% of the launch cost for recouping design costs/profit. This would be $87M/launch
So my really aggressive estimate is still almost an order of magnitude higher, which is why I am doubtful. Lets also remember that SpaceX got $396M from NASA for the development of Falcon 9 and Dragon [1]
[0] https://www.elonx.net/how-much-does-it-cost-to-launch-a-reus...
[1] https://en.wikipedia.org/wiki/Falcon_9#Conception_and_fundin...