Well, no I do not think they will ever be like Bitcoin. They seem to fall out of sight for a bit then climb right back up, I have seen Doge coin go from the 20s back up to the 140s a few times, as to seeing them go much higher I'm not really sure. I think the idea they did start off as a joke makes it hard to find deep pocket investors.
They may never get as much value as bitcoin, If not many people collecting. I wonder if they will decide to burn a bunch to make them more valuable.
They did for a time, so I hear, make it big on reddit as a tool for tipping!