See, I personally do the exact opposite of that. PayPal has caused me more fraudulent bank activity than CC (it may help that my only CC is the debit/credit card from my bank account). So I'll give my CC over the web, knowing that I will know about any fraud when the transaction hits, and I can call the bank immediately - plus I know what retailer specifically did it rather than "PayPal".
Visa Checkout is, just 20 years too late, finally attempting to solve this problem. I'm way more copacetic about Visa have access to my account information since they already do :)
The card companies are shockingly glacial in this market. You'd think the day after Ebay and PP came online, they'd be working on an online card solution. It would have encouraged people to spend billions more on their cards and they've crushed PP in the cradle.
Hardly surprising, entrenched behemoths are always slow to innovate and resistant to change. It's just the law. Ironically, eBay and PayPal themselves now suffer from this.
CC is more cumbersome, because I don't want to give my primary credit card info for random merchants and creating new virtual card takes a few steps.