I've tried using Privacy.com in the past and failed - they wanted to login into my bank using my credentials to verify my account
They've claimed they're working on fallback verification process using two small deposits, like other online services such as Paypal done for years.
I did not observe this. I logged into privacy, added my debit card (which, btw you can set all kinds of limits on so nobody could ever take 10k out) and they took out a small amount ($1.76) which showed seconds later on my bank. I then verified the account and voila, done.
The other downside is loss of some protections, provided by real credit card; it's actually pretty close, the main difference being source of the funds - when somebody charges 10K from your checking account and bank takes a month or two to put it back, it's much more painful in comparison to 10K taken out of your credit card account, even if eventual result ends up being the same. Fortunately you can reportedly set spend limits on Privacy.com virtual cards.
Not 100% true. Almost all accounts allow you to set all kinds of manual limits. Especially for the debit card itself (which is what privacy uses) you can set limits. And the privacy credit cards you generate themselves have limits. My test card for netflix (for example) has a limit of $20 per month.
This might not be the perfect solution (and I have to assume most people have credit cards) but it is better than nothing.
If you want to be really safe, get a master or visa card in your supermarket, add some cash to it and be done with it. But I assume most users who don't have a card don't want to or can't tie up cash in a card so for them privacy should work fine.
That difference between credit and debit networks is in fact what fuels Privacy.com business; the discount rate of 2-2.5% is what they (in part) receive and can even share with you (in the form of cashback). It's similar for Paypal; as long as they (Privacy or Paypal) can limit the risk of chargebacks they earn that difference.