It takes far less resources (time, money equipment) for a Bn of infantry to execute a Trooping the Colour parade than it does a full level 5 BTS BG attack.
Both require precision, dedication, strict adherence to orders, teamwork, and faith that every soldier will do their individual duty to accomplish the collective effort. The difference is that you can do one more often without blowing through your training budget in a month.
I'll paraphrase former Major General Commanding the Household Divison Sir Simon Cooper, who said that parading at Horse Guards was more than just pageantry, it was like being a gladiator coming into the arena. It was a direct call out to the enemies of the realm that this is what they faced should they try to bring harm to the UK: a unified, professional force that will kill you with the same precision, efficiency, and dedication it takes to execute the parade.
It's more than just square bashing for the sake of vanity, it's to build the cohesion and discipline needed to be that force that can effectively and efficiently complete complex tasks as a group.
Does that include the RCAF, RCN, and the tech specialists? Yes. Why? Same reason as above. If I cannot trust that you're not going to cock up a march past in column of route, what confidence should I have that you'll be competent in the performance of your load station?
If you cannot perfect the simple things, the harder stuff will be done sloppily, recklessly, and dangerously