it helps that you can leave them on binance and have them collect the GAS on your behalf and put them in your online wallet.
OH hell no. As much as I like Binance as an exchange, one of the first things I learned on this forum aside from the fact that most members are complete shitposters was that you should never, ever leave coins on an exchange. Nor would I trust Binance to correctly credit earned GAS. When they had NEO down for maintenance for a week (which was about a week ago), I had 9 NEO frozen for the entire week and I apparently earned no GAS from them, i.e., Binance kept the GAS for themselves. And yes, I sent a message to Binance support about it and they keep sending me form-letter e-mails that lead to no solution. So I'm just letting that one go.
NEON is obviously better, but some people prefer exchanges
It is infinitely better than keeping NEO or GAS on any exchange. Please let that sink into your head.
I am more into NEO/BTC as dollar price means nothing for me. I only care about BTC/USD
I fully respect your view, though I don't share it. I can't say I don't care about the USD value of anything, because it's what I use to buy everything with. However, right now I'm not even caring too much about the price of NEO, since I'm in this for the GAS-earning function. In fact, I hope the price stays low for a while longer so that I can accumulate more NEO while it's relatively cheap.