The real question would be "how". A [crypto]asset backed by another currency is easy in principle: simply hold the currency to back it (and make sure you have some sort of transaction fee to cover your storage costs, and don't lie about it...). Same with a [crypto]asset backed by oil or metals. But CPI goods include many goods which are either perishable or lose value over time, and the composition of actual CPI baskets changes over time so you can't do that.

In the absence of that backing you can create a purely synthetic asset that can only track CPI if you've got the ability to withdraw significant quantities from circulation every time the value starts to drop. (That's sort of what central banks do with targeting a fixed non-zero rate of CPI inflation. But they have an economy built on debt so the money supply can contract organically by debts being repaid faster than new debts are issued. This is less troubling for the future of a coin than alternative strategies like having to use VC/company funds to buy back coins, or making a percentage of coins disappear)