Most vaccines require a primary series to be fully immunized.
DPT for kids at 2,4 and 6 months. Booster at 18 months. Second booster ages 4-6.
Hepatitis B at 0, 1, and 6 months
Measles at 15 months and 6 years.
And so on.
The way these vaccines were developed and used, it would not have been possible under emergency use authorization (EUA) to vary from the 21 day or 28 day gap between two doses because EUA requires the method used in the trial(s) that justify the EUA in the first place.
The main reason Pfizer and Moderna were split into two doses was to lessen side effects.
I now think of the two doses as “split dose 1”, and the “booster” (really dose #3) as an attempt to complete the series.
But, new virus and new vaccine, what’s a complete series? No one has any idea. How could they?
But research from other countries like Canada suggests that the long delay between the two initial doses MAY preclude the need for a booster for most otherwise healthy people. (Immunocompromised may be different story.)