It's possible that the muscle isn't fully relaxed, but this is a minority of the cases. This usually occurs with high stress in teens (it's called accomodative spasm), but you will get fluctuating vision, not a steady refractive error.
It's not like you're constantly looking at near and never at far, and even if you were looking constantly at near, the muscle would more likely get fatigued from constantly being in a contracted state (hence 'spasm'). I don't think you'd ever get the case where you would have that muscle just locking into an exactly steady contracted state.

So I don't see what you're really REtraining, other than the facility of changing between contracting and relaxing, which I agreed is trainable. Looking constantly at close for prolonged periods makes the muscle used to being more contracted, and it's a bit harder to relax, but it's not locked into one single point of contraction - it will fluctuate somewhat.
The parasympathetic system can indeed be controlled (e.g. biofeedback), but it's not really like the voluntary system, so I don't think the paradigm of muscle training would hold true for it in exactly the same way, especially since the muscle is smooth muscle, not striated/skeletal.

In the majority of cases where glasses are worn (true myopes and presbyopes), exercises will not help. In myopes, if the muscle is fully relaxed, and you're still myopic, there's nothing you can do. In presbyopes, where the accomodative response (making the lens take on the more powerful state) is decreased, you can't do anything.
Actually even in hyperopes, where the relaxed state of the eye is such that the distance image is not in focus because the eye is underfocused like that, training won't help. You already can compensate for this by increasing your focusing (contracting the muscle), but this takes away from the additional amount that you can focus for when you need to look up close. This works in mild to moderate cases, where you have plenty additional ability for the close viewing, but not with more severe degrees where you don't have enough to overcome even the distance underfocus, and it causes headaches and similar symptoms even in milder cases. And this becomes more manifest as you lose focusing ability with age when you can't make up for the hyperopia.
And for astigmatism, which is a difference in refractive error in different planes, exercises will also do nothing, because you can't do anything to selectively change power in one plane of your vision with the accomodative response.

So training is useless for like 98% of the reasons you would wear glasses for (myopia, hyperopia, astigmatism, presbyopia). I don't see an alternative to refractive correction (glasses, contacts, surgery).