Even if there is "endless" "printing" of 10.000 DOGE per block, this means that, in comparison to the supply, the inflation (i.e. the equation "newly printed coins" / "available coin supply") is lower in each block*, even if there is no halving. This is because the newly printed amount is constant, while the supply increases, so the equation result in a lower value for each block.
"Demand will forever have to increase" would only be true if there were no lost coins at all. Lost coins however are happening constantly. And even if there were no lost coins, as I wrote the demand surplus needed would decrease with each block. Doge inflation is currently 3.727% per year, next year it will be 3.59%, and so reducing over time (in comparison, BTC has 1,5 and decreasing currently, but will sharply reduce to 0,7 next year; that looks better for hodlers of course, but also is a bit an obstacle for "as a currency" adoption).
Doge's tail supply also ensures its long-term security as there's always a reward for miners, and it may even have positive benefits for LTC's security (and thus its price evolution), because LTC's reward lowers like Bitcoin's, but as both coins are merged mined, a LTC miner will always be able to receive DOGE, and vice versa, so it's rational always for miners to mine both.
That's actually what the famous "Stock to flow" theory is all about, and it's the part I agree with - but they build a complete price theory around that concept with a predicted price evolution without taking into account demand, which I think is pseudocientific (in short: because scarcity != supply, scarcity == supply / demand).