Actually it's mathematically impossible. For infinite DOGEs there are not infinite BTCs to sustain the price.
If only any of us would be alive when BTC inflation stops!
Would you consider doge finite if there would be a decision to stop inflation in 1000 years?
Are you aware that cryptos are so new that it doesn't matter jack s what happens 10 years from now, let alone 140 when BTC trickle stops?