I bought a house 9 years ago with my then gf. It was a 50/50 split although I earned more and paid for most of the mortgage and bills. I entered into it believing we would be together long term as we'd had a great 4 years together prior to it. Anyway, when she left me she started proceedings to get as much money as she could. Fast forward 6 months and she gets a big payout from me and I get a bigger mortgage amount to pay off. At this point I said I'd never be put in this situation again so if I ever decided to let someone live with me, no matter how great the relationship my paperwork would be in order and they wouldn't get a penny if we split. Sure, if I married someone things would have to change but I would still protect myself as best I can. Likewise I would want my partner to be equally protected should it be the other way around.
You paint it somewhat skewed, but surely she would have simply been entitled to half the assets from the relationship, which would include half the equity in the house? Why wouldn't she have a claim to that, since you bought and supported it as a couple?
It's not especially relevant that you earned more - a relationship is a joint commitment, whereby each partner puts in a pretty similar "effort". It's a 50:50 thing.
Maybe I'm a little weird but if I owned a house outright (I work from home) and all that was left was usual bills etc I would be drawing up a 'contract' for the girlfriend to sign. I bought the house so it's mine simple as that and no matter what relationship I'm in that would be my view.... obviously having kids would make it different as they would come first.
But owning a house outright isn't an isolated factor in a relationship: there are effects of having that asset which change some important factors. That the relationship didn't/doesn't have to support a mortgage means different requirements of the couple: it's quite likely that one partner (usually the woman, maybe for reasons of social expectations, but also that they are usually younger so earn less), will sack off a career push to play more of a support role. A heavier requirement for cash (to support that mortgage) would reduce the option to reduce the career push, and would likely lead to giving career a higher priority.
Is it therefore fair that, upon breakdown of the relationship, the woman (in your example) would not be entitled to any recompense for her career sacrifice (of which the decision to forgo had been made on the basis of assets held in the relationship)?
E:
just to extend the point: it's not just about career sacrifice. It's likely that, with the security of an owned house the relationship won't save/invest so much (paying down a mortgage is building up an asset). May be that more is spent on such frivolity as holidays, cars, or whatever: it's a decision made with the owned house as a factor. As I said: it's not an isolated factor.