There are alternatives now. You don't have to keep doing business with these colossal assholes.
I run a business which takes PayPal and there's one reason we take PayPal: Everyone has it and everyone expects it.
I'm speaking solely from annecdata here, but in my experience at least, if you don't have PayPal, you're probably giving up a huge potential amount of revenue even if you take CCs via another means.
PayPal makes buyers feel very much in control, if you're doing recurring payments, there's a cancel button, it's easy to challenge a seller and win and they take so many different methods including CCs, bank accounts, "instant bank transfer" (where they'll do bank transfer but fall back to CC, allowing your transaction to go through instantly which many people love). As a buyer, PayPal is very good. If you don't compromise and meet your buyers, selling is a lot harder. Unless someone can make buyers move, there's not much recourse a seller can take.
From my point of view, regardless of my disdain for Paypal as an organization, if you don't accept them and I'm buying something worth more than a thousand dollars, I have no way to give you my money. It's remarkably difficult to pay for large transactions with cash without using Paypal.
When I've done that in the past, I called the bank to have my debit payment limit raised for a short time. It took about 10 minutes, but I don't make >$1000 purchases in cash often enough for it to really matter. Given the rarity, I'd rather make the call than use Paypal.
Necessary evil.
/rant
(Yes, 3-D secure exists, but as a user it's impossible to verify that the site is actually using it before handing over the CC info)
I'd like that for a bill pay system, too. Right now, I have to choose between systems with direct bank account access that can debit any amount, or systems that require manual entry of amounts. I'd like to see a standard where the source of a bill sends an invoice to my bank, and I then direct the bank to pay it (either via direct authorization, or by setting parameters like "automatically pay if less than $X").
We actually had a sane direct debit system here in Portugal, in which the invoice would come with a code that you could input into your bank's site or ATM, therefore authorizing future debits from that company. It was safe, it could be easily revoked, and we lost it to implement SEPA's crappy version.
So you mean they maintain that "perception" by actually doing it. Their business practices are shitty, and they treat merchants terribly, but it's true that as a consumer, it's really easy (maybe too easy) refund and cancel payments with it.
That may not actually be safer, but it feels like it. Though, I would be OK using most of the alternative payment services in this case.
As a seller I use PayPal because they offer two features I haven't been able to find anywhere else: 1) easy drop-in code to add a button to take payments on your site (I'm not a developer) and 2) instant access to cash. Amazon payments offers #1 but I haven't seen anyone else that offers the combo of #1 and #2. Until someone else does, or PayPal decides to screw us (which is a possibility I acknowledge and for which I have a contingency plan), we're still going to use them.