But I still don't see how it differentiates BTC from USD. Because issuing any debt in the first place would inflate the value. So then when you stop issuing debt, the value would get deflated to what it would have been originally. I think this is how the Fed tries to control deflation as well. They print more money, not to distribute it but just so that they can hold it and burn it when they need to control inflation. Either way, both of these scenarios seems like a wash to me. You're just making money so that you can destroy it later.
The only argument I can see here is the idea of having 'wiggle room' within the money supply. In essence a way to control the irrational volatility of the market. If everyone is screaming sell sell sell!, the Fed has a limited amount of room to destroy some money and calm people down before panic takes over. BTC doesn't have that. But even this seems to me like a much weaker 'check' than the author suggests.