Both of my boys are at White House Prep, and I had the same worries about a limited social circle. Obviously I have no basis for comparison, and it depends a lot on personality, but I've noticed a few interesting things.
For pastoral care and academic results, there's no question that smaller classes are better. The kids get so much individual attention, and the school does amazingly well year after year. And of course, it's been a lucky factor during the pandemic, as the small 'bubbles' have allowed the school to carry on, business-as-usual.
Extras like art, drama, music and sport is where it gets interesting. Everyone participates in everything, and there's nowhere to 'hide'. One child will be the school's superstar in each field, without much (or any) competition, and receive the adulation of their peers for being the 'best' at that something. Is this good or bad? Self-confidence is probably a good thing, but you'd have to look outside the school to determine if you're genuinely talented, or just a big fish in a small pond.
Similarly, if you have a penchant something obscure, you'd be unlikely to find a mate who shared your interest. Is this good or bad? Does this manifest as 'cool individualism', or 'weird oddball'?
You're also rolling the dice with the parents. Personally, we've lucked out and found some of our closest mates through the school. But if you're unlucky, seven years is a long time to grit your teeth through all the social events!