Both times, I went from having my own doubts about the relationship, to not caring about those and just wanting to be back together once she ended it. It's just human psychology isn't it, grass is always greener etc.

It’s not about the “grass is greener..” It’s because your feelings of being unwanted are stronger and masking those of unhappiness which you felt in the relationship.

if I'd just ended things at the first hint of things not being perfect, that would have suddenly made her want to work things out and forget her doubts.

For a bit, yeah.

Then we'd get back together, everything would be great and the relationship would be strong.

Until her feelings of being unwanted are no longer there and aren’t masking her unhappiness of being in a relationship with you.

Why is this not a good strategy?

Because it’s a cycle that’ll have to repeat itself to mask the doubts and with each cycle it’ll lose its effect. It’ll probably end up in one of you thinking “wtf is the point in this shit...”