The way I see it, the BF is getting a place to live. He should be paying for it as anyone else would.
In my experience (Sydney) the usual way that this works is that the couple pays a joint share of the rent - one bedroom is one share - and the utilities are split so that each person pays a single share. So, in your case, basically what they’ve proposed.
It’ll also typically work that the share will only last another two months before everything goes to hell and whoever’s the most proactive moves out.
That’s just the local mores, though - it’s probably different in other cities.
Someone once said it’s impossible to share a place with friends. As soon as you move in together, you’re not friends any more.
We do rent per room (based on sq ft) and utilities per person. Whether you want to factor in common areas in the equation is up to you - we didn’t bother.
But everyone also has to agree to any new tenants.
In DC, typically someone renting out a room will tack on an extra couple hundred dollars for double occupancy. So a room might be $600 single occupancy or $800 double occupancy. Utilities will either be included in the rent, or divided up per person.
Not everyone hates living with roommates. Roommates will sometimes be a hassle and conflict is inevitable, but I like having a big busy house and when I’ve lived alone I’ve never really enjoyed it much- with roommates I’m less likely to lounge around in my pajamas all day, and more likely to be active (even if it’s just to get away from the roommates). I agree a third-wheel situation is sub-ideal and new additions to the house should always be subject to approval from current tenants, but there is nothing inherently wrong with sharing an apartment or a house.
There’s a calculator herewhich takes a few parameters (shared rooms, size of common spaces, etc.) and comes up with an estimate.
Rent shouldn’t (necessarily) be 50/50 to start with. It depends on the room sizes and such.