Haven't read the full thread because I can guess where it's been going. OP, when I had small twins and was only able to access buses for transport, I did indeed take the buggy off the bus for a wheelchair user. That's only right because that's what the space is for. This is comment is not about buggy trumps wheelchair or vice versa.
HOWEVER, as a parent of twins my only options were to walk, take the bus or take a taxi (I didn't drive). I could use the overground or underground train because I couldn't get the buggy up the stairs - carrying a double buggy with twins in it is not the same as carrying a single buggy, and escalators aren't an option for twin parents either. The only, very expensive, buggy that was suitable for this sort of thing with newborn twins was a mountain buggy, I believe, and that didn't fit through my front door.
If there was another buggy user on the bus, I couldn't get on, unless they folded up their buggy. This meant hours waiting for buses, or walking for miles. I took the latter option usually and have permanent pain from walking so far post c-section and SPD pushing a twin buggy.
There were lots of other things I couldn't access as a parent to small twins - swimming classes, baby cinema, etc. I had to work hard to get the library and local cafes and music classes to allow me to take my double buggy in.
I needed my buggy. It was my extra pair of hands. I couldn't carry two babies and open a door, or buy things at the counter, etc, etc.
It is really different when you have twins. I don't know if there is more that TAMBA could do to educate - I suspect they don't have the resources.
The good news is, with twins, it's transient, and by the time my DC3 came along I had two little people holding doors open for me and carrying stuff - not that I needed it because I only had one baby. For a lot of people who use wheelchairs, it's not transient. And even though I was on my own with the babies for 85% of the time, I still got respite some of the time.