ok. my 02c
1 You should stay out of any couples business generally
2 You say this person not only lives there, but pays no bills etc ! perhaps he is mad for getting back together, seems like a freeloader.
3 I had a similar situation, OH as you say, did not want to contribute financially, always thought somehow was ripped off, never paid a single bill on any home or mortgage, I am really happy she has gone, as most couples share the load, it is not a mans purpose to be an atm or financial slave for any OH.
4 Without knowing all the details, which none of us & even you will not know (as people conveniently leave out what they want), there is no way to see if it is 100% fair, but from your writing, it seems so, also you say they already split before and they split the proceeds in a way that outwardly seems reasonable.
5 If OH was someone who came to me, the only general advice I would give, would be to cut ties with anybody who is un co operative and resists contributing properly,from my perspective they have issues that will raise again in near future (and seems already there is issues) and they will go through all that drama again, the writing is on the wall, so to speak, if what you say is correct.
It is very normal to work together financially, in fact any couple where one is acting as a single person, I would say the one contributing more should take heed of this kind of warning bell, because I would dare say they are being taken advantage of when 1 person will not contribute.
Also, I will say this, many people are financial dummies, and I see nothing wrong with following a partners requests if they are the financial brains and offering a path to security for the couple, this is not based on sex.