I think the bride’s family can be very understanding of a different financial situation even if they are wealthy or have a million relatives they want to include in the wedding and rehearsal dinner. A friend married a professional football player, but he was from a small town several states away and I don’t think his family had a lot of money. The cost of the rehearsal dinner alone could have put them in a severe financial hole. The bride’s mother just suggested that they have the dinner as a bbq in the bride’s parents’ backyard, and so instead of having to feed 20 professional football players and a lot of other guests in a restaurant, they had hot dogs by the pool and everyone had a wonderful time. Bride still had the big wedding, big dress, big day, but the groom’s family didn’t feel like the poor relatives. I think the groom could have paid (although this was many years ago and I don’t think he made all that much money even as a pro) but in the ‘tradition’, the groom’s family thought they should pay.
I really think both sides of the wedding should cover their guests. My family is tiny, and if we can scare up 10 relatives for a wedding we’re doing pretty good. If either of my kids marries someone who wants to invite 150 cousins and ‘plus ones’ then they are going to have to pay for it.