*She clearly says she wishes her H told her things to make her feel better - irrespective of whether he believes it or not.
And that is something she needs to address in herself.*
I didn't see that anywhere. She said she is bothered by the critical, negative things he says (which also sound unreasonable) and presumably wants him to stop.
Noone has to say critical, nasty things to their partner about their appearance (even if true, which it sounds like they're not in this case). We all practice diplomacy, tact, leaving things unsaid, looking at the positives etc with our partners .. if something really bothered us we could suggest tactfully/constructively ways of changing it (or in extreme cases we could end the relationship if it was really really bothering us and impossible to change, or the person agreed to change but would not get). Ops dh is doing none of those things.
He's mixing compliments and "negs" all the time, leaving her uneasy, upset, confused etc as anyone would be.
I get the impression her self esteem would be ok if she had a decent partner who abided by the reasonable, standard approaches above. He can either say nothing about any perceived bad points, say something constructive and tactful (if they can be changed) or go full hog, decide he doesn't want to be in a relationship with someone with those points and end it ... But he wont do any of those. It's his problem, not her problem (self esteem or otherwise).
Also add to that that what he's saying seems exaggerated or actually untrue.
Also that he's focusing in her looks exclusively all the time.
And he's not getting anything like this from her.