They may be in love, they may be good for each other and they may be the closest of lovers but their relationship would need to be secret which would mean a need to hide the truth from others, decieve people and generally have a constant fear which wouldn't be healthy for them as individuals. So I wouldn't allow it because the external pressures would be unhealthy and unfair.

There are plenty of solutions for this.

If the parents are aware of the relationship, it is as simple as inviting him as "friend of the family" and nobody bats an eyelid.

If they are not, it is harder, but not impossible. Unless either or both are very jealos partners (which points to them having other psychological problems -- do not ever date a jealos partner) they can have, either or both, decoy partners to provide covers. The way gays used to do back when they couldn't come out. Obviously this is best when the decoy knows they're being used as a decoy and accept it; or when the person really also likes the decoy in their own right and doesn't treat them worse just because they're the decoy - this is almost de facto polygamy. It is of course not right to have a decoy while telling them, deceitfully, that they're the one.

Even short of a decoy, if she has a circle of friends who know about the relationship, they can still succeed by just "randomly" planning to be at the same places and times, him, and her group of friends.

So I think this issue, while present, is overblown.

By that I mean I wouldn't allow a relationship that wasn't legal or couldn't be talked about openly.

Although I know my opinion is in the minority here, I really think that you do not "talk about your relationships openly" ever. No matter their legality or social acceptability. Relations are between the people in it, not them and the world. Yes, the old fashioned me comes out like that.