Our school introduced this last year when DS just started Y1.
Initially it made him incredibly anxious. He completely froze up in school for fear of doing something wrong that would earn him a red point. The only thing he ever talked about when he came home was who got how many points of which colour. In a sense you could say it completely took his mind away from learning and focused him on behaving instead, his own and others' behaviour. He didn't need his behaviour improving, it was fine already due to pre-existing latent anxiety, but the dojo made the anxiety much worse.
After a while, after many conversations at home in which we tried to make clear that we did not care one jot about dojo points, and that what matters is the choices you make, not the points you earn (or not), he started to relax about it and now he largely ignores the dojo points. His behaviour has remained the same (or even improved) as he now has returned to 'normal' i.e. is not afraid to say something in case it may be 'wrong'.
I have been a classroom helper and have seen that some children tend to frequently collect red points, others not. This didn't change over the year which indicates to me that these children's behaviour wasn't actually positively affected by the system. Separately and independently some children's parents told me that their children's self esteem was terrible, that they'd often bang their heads on to walls (literally) and state that they 'were bad'. Because whatever they did, however hard they tried, they kept getting red points.
So no, I am not happy at all with the dojo system. However, I must say our school (or teacher) uses it particularly badly. In our school the kid with most green dojos (and no red ones) at the end of the week gains an award. That is wrong on so many levels. It makes good behaviour into a competition between the kids. And a child who struggles to behave well will never win the award. They may give their utmost best for half a day or a whole day but won't be able to keep it up for the week, so will not be rewarded. And once they collected that red point, blocking them from 'winning', they may well give up trying.
Also initially they were constantly pinging. With children gaining 20 or more points each week. Completely distracting from learning. Whereas after a while they made it harder to get green points, so the weekly winners would have 6 or so. And sometimes they made class rewards dependent on no children having red points, so children who did get a red point felt bad for spoiling things for their mates.
All that said, I think the dojos CAN be used in a more positive manner. E.g. rather than making it a competition between the children, you can set each child individual aims. You can tally up and set back to zero after half a day, rather than making yesterday's behaviour hang over your head (and be displayed for everyone to see) every day. Children who find it hard to sit still can be told they will gain points for sitting still, while other children won't - but each child can be aware of their own individual target/goals. You don't have to actually use red points, you can use green ones only, and this does have a good side: You can have an immediate positive reaction to/recognition of small positive things throughout the day. Children who behave well generally can still have goals and be rewarded.
Of course you can do those things with or without the dojo things. So, as with most things, it depends not so much on the system, than on how it is used. And if you talk to school, I'd focus on this aspect. Suggest ways how they can use it more positively.
The main problem IMO is that teachers using the dojo system tend to stop thinking. They feel 'oh this is how we are managing behaviour now, ok then' and just start using it, rather than thinking about what they really want to achieve and how they can use the system to do that.