Look. I'm a letting agent. (Most hated profession on here but hey- i can take it).
HB can be a pain in the arse. They take ages to make decisions, if something changes, they can adjust the amount paid to reflect overpayments and they have a tendency to just stop paying. Not to mention that they rarely pay enough to cover 100% rent and chasing tenants for top ups is difficult and complicated as the payments don't tally. (Rent taken in 12 advance monthly instalments, HB paid in 13 arrears 4 weekly instalments).
If they find the claim has been made fraudulently, what they do is they then take it back by actually not paying other claimants.
For example, letting agents get one lump remittance for 5 tenants who are claiming. Tenant 3 turns out to be fraudulent. HB stop all those payments as in their eyes the letting agent is one landlord and they are recouping their lost money. Just imagine what that does? Letting agent has to pay out to the other 4 landlords.
As usual, it's the few fraudulent claimers who screw it up for the rest.
Other problem can be that if a landlord needs to get their property back and the tenant wants to get social housing, they are advised to stay put until they are evicted by court order, otherwise they would be deemed as being intentionally homeless. This means costly legal fees and uncertainty for landlords. Ultimately, the landlord is the letting agents client.
For what it's worth- I totally agree about your general frustration etc. But I don't agree about it being sex discrimination.
I am also a private renter, a single mother and a HB claimant by the way!