For me, one of most important problem is the inability for small payment processor to enter the field because now if amazon, eBay, steam, etc... don't include your payment scheme you're better be ready for a though (impossible?) battle. That's one reason the payment industry stagnate so much.
On top of that, all these different payment systems have different fee structures, so it's unclear how this could be completely in the user's control, since the merchant probably won't be happy to accept arbitrary fees, unless the fee was levied on the user, rather than the merchant, which would be a pretty big difference.
As an example in Switzerland most online retailers allow you to pay with a Postcard. ( https://www.postfinance.ch/en/priv/prod/card/pfcard/direct/o... ) I would have hoped that PostFinance, the issuer of the card, would be able to implement some standard that would allow it's client to pay retailers that implement such standard.
Switzerland has only 8 millions inhabitant, It's certainly not enough to convince big tech companies to add it as a payment option.