Otherwise many wealthy people could buy a nice pad, install a non-working dc in it and get housing benefit
It doesn't work like that.
As a topic for my Mum discuss at her community action group, we both did a lot of research about local rents, LHA rates and the complete lack of property available at an affordable price for people who are claiming LHA.
An average two bedroomed property where I live costs between £750 and £1,100 PCM to rent.
Today on Rightmove in my area there are 15 - 2 bedroom properties available to rent.
Out of those 15, only 5 of them do not state No DSS / HB / LHA or No children in the advert.
These 5 properties range in rental from £750 PCM to £850 PCM.
The LHA rate (2 bedroom) for my area is £663.09.
So even if somebody managed to get a tenancy on the £750 property, LHA would only cover £663 PCM and the tenant would have to pay a top-up of £87 a month.
£87 a month rent top-up may not sound like much but if you are on benefits like IS or JSA, this amount is a big percentage of your income.
No private LL is going to rent to someone at LHA rates when they can get much more money from someone who is working.
This has meant that parents like the OPs feel they have no other option than to buy an investment property specifically for their child to rent.