The $100 Android phone might have a superior interface, but it's going to fall foul of Android's native up-sampling unless you're using something like UAPP to bypass that (an approach that comes with a variety of other issues and doesn't allow you to use things like Spotify without getting nobbled with ASRC either). If quality is your primary goal, which I'd assume it is if you're bothering to carry a Mojo around in the first place, most people want to avoid that up-sampling. Most DAPs make that easy ... unless, of course, they're based on Android and then it becomes implementation specific.
A DAP also offers the ability to run a high-quality, high-capacity (many DAPs have multiple slots which is a boon for those of us that don't want to browse by folder), playback solution that does not require we take a Mojo (or other external DAC) along if we are traveling light.
And then, yes, there can be differences in sound quality even when you're not saddled with forced up-sampling. Depending on how you interface to the Mojo that can be a meaningful difference ... e.g. USB is not the best way to drive a Mojo and no phone I know of has either COAX or optical outputs.
So, no, a DAP isn't useless with a Mojo - even if ALL it got you was more on-board capacity. But, as it stands, DAPs offer other benefits to phones as a source for Mojo or any other DAC.
If a phone and swapping cards works for you, then more power to you, but it's not even close to a palatable solution for me.