If you are suitable, a rescue will let you have a dog.
But many people here are telling you that this isn't true. I AM suitable. Have been for about 20 years. I held out, really wanting to rescue a good old fashioned Heinz. The kind of indeterminate mutt DH and I were both brought up with. When I realised that they are few on the ground, there were mainly 'posh' puppies and older dogs, we decided that we wanted a medium sized dog that require 1 - 2 hours of active exercise a day. Not fussed about the breed or age. We had time and space and easy access to dog trainers and behaviourists where I worked.
For 15 of those years we had a large, well secured garden and lived rurally, lots of rambling walks, no noise, kids etc. And nope! Despite working for a rural college with doggy daycare, trainers, etc .The fact that I would walk the dog across a rural campus every week day was not good enough. DH worked away and that would be too confusing. Oh, and the home checker who got lost and just pissed off.
I know you are defending something you obviously love, but at some point, you are going to have to realise that quite a few of us have fallen foul of some kind of purity spiral where rehoming won't take place unless the individual and their home is perfect. And the reasoning is not always clear, often seems to be a judgement that there can be no questioning or discussion over.
Whilst I wholeheartedly agree with you over backyard breeders there is going to have to be some kind of acknowledgement that, currently, the intransigence of some rescue centres to actually rehome has played its part in their continued existence and lockdown growth. Enough posters here are telling you that this is the case.