The way I have always thought it should work is that, GM take priority/first contact and then secondry regiments like 501st/212th get involed (And non CQB/Combat regiments like Shock,GC,WP,38th ETC fuck off unless explicitly asked for).
GM often just die first if they go alone and so 212th/501st seem like the one breaching. This is why GM don't breach alone and why they use all regiments not just donator like some are saying. Breaches are a difficult thing to do and without a ton of equipment to help them doing it alone is hard. And small breaches never happen unless you are talking about small rooms... which everyone does. So big breaches is all GM have to lead (which need other regs to help)
Anyway time to ignore all replies to this comment