Of course not. The bulk of the budget for the Navy and Air Force is mostly for the homeland. Yes, we do deploy some naval and air forces to NATO missions but the bulk stay here.
The army is our primary expeditionary force and only a small fraction of that is deployed in support of NATO at any given time. The bulk is here in Canada training for missions that could be anywhere including Canada. Add to all of that the heavy administrative overhead presence safely ensconced in the Ottawa Valley.
2% is everything, lock stock and barrel.
Yeah, it may seem that way to you but I think in reality, the Europeans want to see a Canadian flag on the maps of their borders so that they can see that the Canadians are in it for at least a penny, if not a pound. There's a lot of symbolism in that both to the Europeans and as one of deterrence to the Russians. More importantly, it gives you a measure of street cred when other issues such as trade, come up.
Let's be honest. A mostly fly-over brigade is cheap in the long run and adds a significant benefit in focusing training and providing a positive morale issue to enhance recruiting and a raison d'etre. (and no! I'm not considering six month rotations as a positive morale issue. - That needs adjusting)