They need to cap the dogecoin endless cap. If they want it to have any value at all they need too.
The doge inflation is arond 6% a year, and will be smaller year after year. It is far from being one of the main reasons of the Doge downfall.
The inflation will remain 10K Doge per block after the final halving, so it is a linear inflation and the inflation expressed as a % will drop every year.
The total number of new Doge entering the economy is:
365 * 24 * 60 * 10000 = 5.256 Billion
So the inflation over the first decade is:
5.26%, 4.99%, 4.76%, 4.54%, 4.34%, 4.16%, 3.99%, 3.84%, 3.7%, 3.57%
So the total coins will be 150 Billion in 2024. The inflation of Dogecoin tends to 0, while for fiat it stays the same more or less.
The main advantages I see in Dogecoin is it's very low price, merchant acceptance (network effect), very very low transaction fees and confirmation times, 10 times the transaction capacity of Bitcoin. There is a Counterparty style project build on top of the Dogecoin blockchain: Dogeparty.
As others mentioned, it is a low-end and cheap coin, with good enough security (AuxPow) that will not easily die.
I believe that Dogecoin will stay in the top 10 in terms of market cap and trade volume.
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