Overweight and unfit are different things. Being in control of one's body can be a different thing as well. Some people aren't in control of their bodies. For some people, it doesn't matter what they do, they will never be a Victoria Secret's underwear model. Personally, I could see that struggle against one's own body as being a positive characteristic of a trainer. I wouldn't necessarily care if someone had gotten to the end of their struggle so much as I think I'd want someone who really understood that struggle and fought against it (and continues to do so). After all, it seems like a main component of seeking a personal trainer is to get help with the motivation to overcome whatever personal struggles someone has.
Conversely, I can see situations where a trainer looks amazing, but it may just have always come naturally to them. They may have never been unfit and have no idea what that is like. I think the inability to relate to someone's struggles could be detrimental in terms of being a helpful motivator.
Similarly some people look good, simply to look good. They may not always, or ever, care about fitness or health. In some cases they may actually do unhealthy things simply to look good.
I'm certainly not saying that anyone fit or who looks good is a bad trainer, just that if I were looking for a trainer, I'd care about attitude first and foremost. If they can squeeze sweat out of me, and be positive and uplifting, I don't really care if they are 400 pounds.