Towards the end of my DJ'ing career, I was to the point of showing up to a venue (that had an existing sound system) on my motorcycle with my controller, headphones, microphone (that didn't smell like beer breath) and laptop in a backpack. I'd just plug in and go. But even then the idea of DJ'ing from just a phone or tablet seemed weird to me. I understood the appeal of it but....
The sticking point for most people is stereo. When you throw on AC/DC, you expect to hear the guitar out of the just one speaker but when DJ'ing a large room that doesn't work. Half the room hears the guitar and the other half just hears high hat. So you end up flipping the mono switch, ya know, just for that one song. Then eventually you've done three gigs in a row and realize that it's been mono the whole time and no-one noticed, not even you.
Headphones jacks have two audio out channels. We typically think of them as left and right, but they aren't, that's just how most people use them. Once you get past the mono idea, you realize you have two distinct audio outputs on your phone or tablet. If the music software can do the mono summing instead of the mixer, then then you can hook the "left" output cable to mixer ch 1, and the "right" to ch 2, and play different songs out each. Make sure the same output of the mixer goes to both speakers and you're in business. You just need dj'ing software that can play two different songs at the same time on your phone and interface with a controller, probably via bluetooth.
Now you can show up to a party with just your phone that you were already carrying anyway, plug in to their controller, and make a surprise appearance.
It still weirds me out, but modern phones have the horsepower to do this. They certainly don't have the disk space for a terabyte library, so you aren't going to work a six hour wedding with an iphone, but there are TB SD cards so certain Androids could certainly do this.
There's probably also software that will do everything over bluetooth so a completely wireless phone could work.
I've been out of the game for over a decade. I can't imagine how far the controllers and software have come and don't want to find out because I'm sure my poor wallet can't handle it.