'Forcing' horses is only one cause of problems, being overenthusiastic, hyperactive or insecure about what a movement should look like can cause gaits to differ too.
And yes, I do reward the regular gaits too, especially because of all those reasons (and because all those reasons exept the first of course seem to live in Sjors' brains... ). For example, if I ask for a passage-like movement three times after another and reward those, Sjors tends to replace all regular trot by this gait. And walk and halt and canter too, by the way, if you let him.
So instead of following that road, I ask for one or two passage attempts, and then as for a regular trot and reward that too, so that Sjors realises that passage isn't better than trot and that the first should replace the latter.
And of course the regular gaits are the basis of Haute Ecole dressage too, so if 1/5 of our training exists of special exercises, the rest exists of walk, trot, canter, and sideways movements in these gaits (well, only in walk and trot still
). By the way, these sideways movements, especially shoulder-in are very good at loosening your horses' body too when he tenses, over-collects or chances his gaits for the worse.
Another very good thing to 'restore' gaits that have changed due to too much thinking or overcollection (offered at liberty by your horse of course) out of enthusiasm, is ask the horse to lower his head and neck again during that gait. That loosens the back and turns the gaits back to normal again. Sjors sometimes turns his walk into a kind of pace when asked to collect in walk. When he does that, I ask him to stretch his neck again and if he responds, I reward him.
The last thing is: put everything on cue as soon as possible to avoid confusion and with that confued gaits. That is quite hard if you have a very smart and expressive pony who really likes to show off everything that he just thought of (like Sjors again), but especially in those cases very important.
By the way: a four-beat canter is not seen as bad in classical dressage - it's only forbidden in the modern, FEI dressage competitions.