a dollar is a bearer bond that can extinguish a Dollar of DEBT, debt in the form of taxation is a big part of that, but also legal tender laws mean ANY private debt can also be extinguished by the dollar. So the dollar is the universal extinguisher of all debts in the U.S. and that is it's backing.
I've argue in other threads that the BTC computer network or even the cryptographic code of BTC dose not constitute backing for BTC, because it dose not establish any price or valuation for BTCs.
But being a universal extinguisher of all debts does not establish any price or valuation for USD either. Nothing that's backed by anything else does, because all price is arbitrary. A gold-backed currency could be backed by an ounce of gold, or a gram of gold, and could be numbered 1, or 5, or anything else. Likewise, the government backing, or the extinguishing of debt backing, could back a dollar that can buy you a burger, or a dollar that you would need 1,000 of to buy a burger, and the mechanism would be the same. So backing isn't even "propping up."
Personally, I see backing as an IOU - a liability - where the thing that is backed has a promise from someone else that they will give you something in return. A gold backed currency is just an IOU with a promise to exchange it for some arbitrary amount of gold, and a government backed currency is just a promise that the government will forgive your debts if you exchange it with them. This is why non-backed things, like land, oil, gold, or bitcoin is so much more powerful - there is no one that needs to make you any promises. The land will let you build on, the oil will burn, the gold will be yellow, shiny, and highly conductive, and the bitcoin will work on the blockchain, without anyone promising or allowing it to happen.
In a sense yes the 'universal' nature of the dollar isn't establishing a value either, BUT nominal price stickiness and size of the US economy create a lot of stability in the value of the dollar, not to mention a central bank which acts to keep inflation (price inflation) to low levels (yes you can have as much or as little faith in them as you like). I've never said that the 'backing' of the US dollar is perfect, heck it might not even be considered 'good', you can disparage the quality of the backing as much as you like but you can't say it's not backed.
It simply HAS a backing is all I'm saying, their exists a structure that tries to guarantee a future exchange value, BTC doesn't have any kind of guarantee it just has an exchange market that can go to incredible extremes (bubbles or total collapse) with no brakes on it. If their were even something like a group of people with large wealth that were publicly pledging they wouldn't let BTC drop below some floor price that would be a backing but we don't even have that.