Inflationary cryptocurrency can have rising price, e.g. Monero or Dogecoin. Inflation must not be too high. What if proposed cryptocurrency had emission increase with difficulty, but returns will be diminishing. For example at the start diff increase is 1 coin per step then, 0.99999999 per step, and so on till it stays at 1 satoshi per step.
Monero is a good currency, but in terms of price (and despite its multiple uses), we are almost at the same levels as in 2017.

Regarding Dogecoin price, I think the chart below is sufficient to explain everything.

Price is not the important factor here, but rather the cost of a successful double-spending attack.