Paul - - here's why.
When I was 18-19-ish, I played at a muni outside Buffalo. It cost $60 per year if you were a town resident, and the course was 5 miles from my house.
We didn't have a lot of money, so I picked a used two-wheel cart and used to chain it under my bicycle seat and it became a trailer of sorts to get my clubs and me to the course (Brighton in Tonwanda, NY).
I used to play 36 when I could and then put the whole contraption together again and ride back home. Those were great days.
But somehow the thought of a college kid riding his bike to the course with his cart, and then using the cart probably doesn't sound very high end to some old-school blue bloods... You know the types - they've been on their club's BOD for a gizzilion years and they get upset if your shorts are too long or your gal's shorts are too short.
And therein, I feel, lies the pidesposition among many clubs against carts - I think some ill-informed members find them to be too low-class, too "muni" for their establishment.
Of course it's nuts. But I'm pretty sure that's where the anti-push/pull cart bias comes from.
Now, if the club wants to make more $$$ off power carts, that's fine - but let a player that wants to walk with a cart do so.