If IOU’s are being used to indirectly exchange present goods and services, then this debt IS money, and there IS inflation. The inflation is not from one CD being used as multiple payments. It is because if CD’s were as good as cash, cash would disappear and CD’s would be the standard money. All cash would be turned into CD’s by banks. Banks would keep lending out the cash they received in exchange for CD’s, but the recipients would quickly convert to CD. People would not redeem CD’s - they would roll them over, or request new ones. CD’s would become exactly like demand deposits currently are, being issued expansively against a static or less-slowly-expanding cash/demand deposit base.
Why? If CD’s are accepted as money, there is no point to use cash. CD’s earn more interest than cash, checking, NOW, and other spendable accounts. They will never trade at a risk premium because they are ensured by the government against the bank’s failure. They will never trade at a time premium because there is no time premium between a present good and another present good. The only reason the time premium exists to begin with is because CD’s are not accepted as a general medium of indirect exchange.
The only difference between CD’s and demand deposits is that CD’s are not legal tender and are not necessarily instantly convertible into such; however, their payment of interest may partially make up for this.
What we are missing is that banks and governments alone do not create inflation. People’s willingness to accept additional currencies denominated in the same units, including debt instruments, is inflationary. This willingness may come from government guarantees, but the only reason government can do such, is because people accept government. They supply it the means they need to suppress dissenters.