As soon as doge is the most profitable coin, it will be mined by ASIC farms and multipools and then dumped on the exchanges making it not profitable again. So I think it's about time for the DEV's to really think about capping the coin as it was introduced in the first place, maybe change the PoW algo, and hey, why not also implement PoS? Of course that would need a hard fork, but it's possible without problems.
Do not let such a great thing as doge just slowly die...
What you mentioned is already happening. The good thing with doge is that it has a huge community to support it. Thats what makes it have a future for me. But if you think about it twice, changing the algo os the PoW sceme it would even have a negative effect. Do you think that the price of it would be the same if anyone with a computer was able to mine?
The value of it isn't based on how it is mined. The value is based on how much money people are putting into it, which is in effect based on its usability. If DOGE were accepted everywhere (like a MasterCard), its value would be significantly higher than now since it would have a real purpose and use. Don't confuse this with PoW/PoS/Premine/whateveryouwant. Two very different things.