I also agree with the OP, and would find it both offputting and inconvenient to have to resort to snail-mail to open an account somewhere. We live in an age of ever-increading consumer choice and convenience. Subject to all the other essential criteria, safety concerns and due diligence, of course, for myself I'd choose a broker willing to handle the matter online, and I would expect to find no difficulty at all in doing so.
I just opened my account with Tradestation. I called in, talked with a rep. for close to an hour about their commissions, fees, platform, etc.. just about anything I asked he answered. He then emailed me a link to apply online and now all I have to do is send the wire transfer. Couldnt be happier with my experience so far with TS. Also, he has offered his availability through email, which is great. I am switching from Fidelity, in hopes of becoming a more active trader.
My experience with AMP has been excellent. Almost 2 yrs now. They are very responsive to any difficulties. Businesslike but courteous and efficient.