That player count recommendation is based on my personal GMing style. I have GMed Beam Saber for 5 players before, and in those games I often feel like I can't provide enough spotlight on any of the characters. It feels very much like "alright, you did your action, but we can't really follow up on it because it's been too long since this other player has had the spotlight, so we're going to jump over there and EVENTUALLY get back to the follow up on what you just did."
If you aren't concerned about that issue when GMing, then the other considerations are that the Squad will have more resources (stress, quirks, gear, Harm/Damage, etc) to spend in each Mission, and that the game doesn't scale Supply Point income with the number of Players. This means that individual Missions won't press the group hard, but that what they do spend will be harder to recover, giving the game a stronger sense of The War being one of attrition.
Hope that helps.