Is there any harm done by a shorter interval? Like, does 3 weeks and then a booster at 6 months result in less protection than initial shot + 2nd at six months?
That three week shot may not be optimal for long-term immunity, and may be redundant if you have the later 3rd shot, but it does provide some shirt term protection.
In the case of the HPV vaccine, I can have my 10 year old wait the year before the booster because long-term efficacy is the goal. With most childhood diseases, herd immunity provides grace… But COVID is rampaging now, so unless that short interval permanently damages your immune response to the vaccine, it seems better to just go with a three shot regime.