I'll play devils advocate here and suggest Shelter, The Wallich illustrate the 'numbers' to garner public support and funding?
Shelter was established in 1966, their aim to stop homelessness. Not doing great are they?
Not sure if it's still the case but pre pandemic Cardiff had enough capacity in temporary accommodation that no individual needed to sleep rough. Covid meant every authority had to find accommodation for everyone and priority need was binned off.
The truth is Cardiff City Council would love to end homelessness in the city centre area as they feel the population of rough sleepers contribute to ASB and crime etc.
The sad fact is they do, councils are then given a choice to either engage them into services or criminalise them. In reality Cardiff City Council in the recent past have done both, like most Welsh authorities. The homelessness issue is a complex one, far too to look at it as simply as it appears you do.
I'm no fuucking Tory.