Blue Moon is closer to "right sized" for the moon landing mission. Even if boil-off wasn't an issue, Starship needs so much fuel simply to haul its overly large inert stage mass from the Earth to the moon and then up and down to the moon surface. Add in the boil-off (TBD but definitely not zero) and subject the whole mess to the tyranny of the rocket equation and it is simply a ridiculous exercise. Musk is dreaming that he can leverage HLS to get the taxpayer to pay for his fleet of Mars Starships, but I think physics will thwart his efforts.Without way to actively cool the propellant, I don't think the HLS will go anywhere. Even just sitting on the lunar day side for hours would be wasteful then.
Of course, you need to determine the needed power of that cooling unit....
The Blue Moon lander also includes such a feature.