I think this is a really good idea for the game; others and I have suggested it before. I believe squad awareness is something that is somewhat lacking in the way players approach this game, so anything that could boost that might help.
I don't necessarily fully blame the game. With the rudimentary leadership/squad system in place, players have more than enough at their disposal to actually play on a team as squad members should, with different squads playing different roles, they just often largely choose not to. Even I am guilty of this on occasion, but really only when my squad leader just seems to be playing solo with no effort at communicating orders, throwing smoke, trying to use the squad leader spawn system, etc. I suppose I should always try to switch squads in such a situation.
The best rounds in RO2 are where TLs and SLs work together with each other and with their teams and the squad members mostly try to follow orders. When this occurs, even getting stomped for a loss is way more fun even than winning with no teamwork.
Another thing that I get the impression hurts team/squad play is the general hurry to get into the action that every round seems to bring, the "I don't know what squad I'm in, I don't know what I'm supposed to be doing, so I'll just pick an objective at whim" w-key+shift spam. I'm not sure of the details for this idea, but I feel that every match, maybe every round, should come with a short "briefing" period where team leaders and squad leaders can deliver orders both with the order dialog and the voice chat, but nobody can otherwise move or do anything, and before the round timer starts. Some kind of short time for a TL to actually ask the different squads to do different things without the pressure of the round timer having started.