I would guess they just want the personal satisfaction of getting as many people as possible out enjoying the roads.
Yeah, but if they organised entry through another mechanism they could make the ride effectively £3 cheaper and get more riders out on the roads. Or have £3 more to spend on cake for riders. Or £3 more to spend on cake for themselves.
(I'm talking specifically about events where non-members greatly outnumber members)
You asked for a reason why Audax organisers might continue to run these kind of rides as an Audax and I gave you
one answer.
Are you trying to tell me this is wrong somehow? I'm not sure what your point is. People run Audaxes because they want to run Audaxes.
Sure, one could take various Audaxes and run them under different regulations and get way more people riding them, but that's not what most Audax organisers are trying to do.
It's along running trope that you could take a mildly hilly 200, rename it the "Surrey Hills Mega Bastard Sportive 126", charge 10 times as much and throw a few gels/bananas/carb-drink at people at various points, a shitty goody bag at the end, and promise gold/silver/bronze time bragging rights. You might get loads of entrants, some even may come back to ride it again the next year. Woo, popularity.