Yeah, I genuinely hate whenever that saying goes around.
After more than a decade of constant therapy I've also come to the conclusion that a partner would actually help me battle the exact issues that I cannot seem to overcome by myself. I'm convinced that this is also the case for the people I know myself, who have severe lack of self esteem but are still in happy, long-standing relationships.
A partner can help you understand that there is nothing wrong with you, that you can be loved, that you are lovable and deserving of it. Cutting that possibility off is just stifling and honestly real shitty to see for folks like me.
E: Just saying "you need to work towards loving yourself" is all cool and good, but it's simply not always possible to make much of a headway towards that. Some folks are just fucked up, and they still deserve love, and it is still absolutely possible for them to find a relationship that is satisfying for all involved.