No! No! And no again!
Chakotay was good as he was.
In fact, we do have two possibilities:
1. A Maquis Commander who realize that the best chance for him and his Maquis fellows to get home is to join Voyager, play by the rules and have a decent chance to come home in the future.
2. A whiny crybaby who ruins all possibilities for the Maquis on the ship to have a possibility to come home and maybe be paroled when they do arrive home.
We can also compare the both crews on Voyager with the horrible mix of people on the starship Destiny in Stargate Universe:
Voyager: Two crews led by a smart Starfleet Captain and a smart Maquis commander who realized that cooperation between the crews is the only way to survive and get home.
Destiny: Two crews, the military and the civilians who spent most of their time arguing, fighting, manipulating and whining, led by persons who were hardly capable of commanding and steering a tricycle.
No surprise that Voyager managed to get home and Destiny didn't.
Complete harmony and complete pointless friction are not the only two options. For instance, I liked the way Chakotay talked Janeway into making B'elana chief engineer. DS9 pulled it off with Sisko and Kira and Voyager arguably had more natural conflicts they could have worked with. In Learning Curve, Chakotay could have been a mediator for his crew rather than just stupidly punching someone and saying "THAT'S THE MAQUIS WAY OF DOING THINGS! Now you spend the next 70 years doing whatever Janeway says period." He could have brokered an arrangement where the Maquis crew had to do the training but got leeway on the dress code. Chakotay could have also been taking the position more often that Starfleet rules don't apply dogmatically when you're on your own in the delta quadrant. They abandoned that entire narrative after Alliances because one group of people were murdering jerks.
If they had found the balance where Chakotay was keeping his crew under control but also advocating their position to Janeway he could have been a much better character.