Why is scarcity required for collateral? If someone has to pay $20 to register a Twitter username and also risk losing their username for abusing reporting, is that not effectively the same thing?
1. Scarcity is required for value. If there was an unlimited supply of Dogecoins and anyone could have as many as they wanted, they would be meaningless.
2. Value is required for collateral. If you don't value an item you are risking as collateral, there is no risk and no value, and the item is useless as collateral.
3. Thus: scarcity is required for value, and value is required for collateral.
As to your question about using $20: yes, it is effectively the same thing. There is scarcity for dollars and they have a "use case" that is off the charts (i.e. you can exchange dollars for virtually anything you want), thus they are extremely effective as collateral.
Your question is obviously, why not just use dollars, then, instead of crypto? The answer is the same as why bother with crypto at all? What's the point of crypto? Why not just stick with dollars for everything?
The answer to that is really long and I'm not sure I could do it justice. Briefly, crypto has some definite advantages over dollars. The scarcity of dollars is artificial: the Government can simply print more anytime, whereas something like BTC, the scarcity is hardcoded into the system. Control of dollars is extremely centralized: dollars are controlled by a very small group of people within one government, whereas BTC is much more decentralized. The advantages of a decentralized over centralized monetary system should be obvious. There is an entire class of middlemen imposed between you and your dollars: i.e. the Banking System. The Banking System has enormous power over you and your dollars. Crypto purports to cut out the middlemen and put control of your money directly in your hands. The list goes on...
Edit: Realizing I didn't really specify as to why Musk would specifically choose to use something like Doge for twitter. I can only speculate, but here are some interesting thoughts: first, if you are charging "dollars" for things, it opens you up to a whole bunch of rules, laws, and regulations that don't currently exist for something like Doge. In short, Musk would be much more free to do what he wants if with a non-dollar token system like Doge as a method of value exchange. Second, like I said before, if you are a pro-crypto person (like Musk) and want to see the proliferation and legitimation of crypto, putting the world's number one communication platform on a functional crypto system is a HUGE step in that direction. Third (and most succinctly), Musk owns a fuckton of Doge. If Musk manages to actually incorporate Doge into Twitter, his investment will skyrocket in value.
Those are all reasons why Musk might want to incorporate Doge into Twitter. But then you'll want to know why average twitter users should give a shit about using Doge? First, using some form of "skin in the game" system definitely does have the potential to clean up a lot of the bullshit out there now. That benefits everyone that legitimately uses Twitter. You could also do that with dollars (like you mentioned), just not as easily. Second, a token system like we are imagining gives twitter users the chance to actually earn money (in Doge) through twitter. Users with popular posts or maybe users who are good at sniffing out spammers could make money- theoretically really good money- just by using the platform. That's the basis for Web3. You just can't really do that with dollars, but you can with crypto.