HA properties are rented out at a much lower rent, than if that person was private renting. That's the whole point of HA properties, providing housing for those who can't afford to pay market value. A proportion of HA tenants will be having some or all of their rent paid for by Housing Benefit.
If you don't pay your rent then you can be evicted, regardless if your private rent or if it's HA (although my guess is the threshold for HA eviction would be higher). In the same way, if you default on your mortgage enough times, you can eventually have your home repossessed by the mortgage lender.
Private landlord can decide to sell, and the tenant has to find alternative accommodation. HA means you have a secure tennancy and don't have to move, regardless of the size of the property.
We have a housing crisis. There are fewer private landlords, and rents are extremely high. There aren't as many family HA properties available with 3+ bedrooms. If a family were given a 3 bedroomed property to raise their family, by a HA and the children all grow up leaving the parents alone in the property. I don't think it's unreasonable to insist that that secure tenancy is now passed over to a 1 bedroomed home, so the 3 bedroomed can be given to a family. I'm not suggesting the parents should lose their secure tenancy but it should be passed to a smaller property.
In essence a HA property or a private rental property, isn't your own home. You don't own that property, and therefore sadly, you can't expect to have exactly the same security/stability as someone who does. Although the Renters Rights Bill may change some of that.