The only thing about a dental implant, isn't it the case that they are completely fused to the bone and so can't be tipped/moved with braces? Or does this not matter if it's one of the posterior teeth? You know the way the inclination of the front teeth has to be de-compensated before surgery - are molars always left alone?
Could you explain a bit more why crowns are such a bad solution? I don't doubt what you're saying, it's just that I don't know that much about this area.
I think if you need braces (which probably you need considering your original post) first get the braces, then when the teeth are all positioned, you should get implants.
Crowns are bad because they dont stimulate the bone under them. Which might lead to bone degradation. Since the jawbone's role is to support the teeth, and every bone needs constant stimulation (in this case, chewing) not to degrade, especially true for the jawbone. If frontal teeth are affected the whole thing is more obvious since the chin collapses inwards which causes that kinda weird look some old people have who couldnt afford or couldnt have implants.
If you have one teeth its not that obvious ofc but if you can afford it I might consider it as implants are also way stronger than crowns.