Hostels are for this market, no? Share physical infra (bathroom/heating/walls) with other humans (aka strangers) and you get the same family discount. You're not obligated to pay the premium unless you want your own bathroom and own personal space like families tend to want
As in: families don't get a discount, they just amortise the cost of privacy that you also seem to specifically need/want. but many solo travellers don't care to pay for that.