While in principle that's clearly sound - fewer viral particles means fewer future variants appears to be the consensus opinion - I'm skeptical that the decision to recommend boosters after 8 months will have a measurable impact on that.
First of all, even under rosy vaccine acceptance trajectories that's not going to be many doses vs. the unvaccinated population; secondly, you need 1 dose for a booster, yet 2 for a full vaccination; thirdly, the data for hospitalisations may not be in, but for mere infections it is clearly showing a reduction in efficacy well before a that 8 month mininum so the opportunity cost of not vaccinating half a person will be offset in terms of transmission by the booster dose; fourthly not all vaccines are easily distributed, and as long as the US needs to have a readily available supply to entice the unvaccinated stragglers, you might as well use doses nearing expiration dates for boosters rather than throwing them away; fifth: we're not at 8 months yet for most people, and if the minimum delay is 8 months the average might be considerably more such that by the time this matters vaccine production should be higher and thus the loss relatively less impactful.
Some of those effects might be trivial or zero, but at the very least the small number of doses overall affected probably isn't. I'd be really surprised if the US reaches 100 million booster doses by next spring; and even if we did that's just not a huge number if your aim is to reduce transmission (as opposed to suffering).