No it would not be better, it would be a disaster. The Army (and especially Marines) are trained to the point of muscle memory to respond to aggression with overwhelming deadly force. It's not a good idea to task them with handling protestors like it's not a good idea to task a trained fighting dog to play at a dog park.

what is ICE in this trained dog analogy?

Dog poo?

Or, a pack of angry, trembling chihuahuas that keep on attacking dogs with certain colour fur.

Come on now, by this logic marines should not be allowed to live in the US at all as they couldn't be trusted to go out in public without strangling someone for doing something that they deem a potential threat.