I think it's a matter of preference. It's easy to give too much or too little water to a very small seedling in a big pot. With a solo cup you just soak the grow medium and the roots get a lot of both oxygen and water at all times because the medium dries out quickly.
The downside is you have to transplant a seedling as soon as the leaves reach the edges of the cup, or its growth starts slowing down. Also, if you're not careful you could possibly shock the plant during transplant.
I've done it both ways and seedlings started in solo cups definitely grow a little faster at first, but just for convenience sake I usually start my seeds in something like a Rapid Rooter, then plant that directly in the final container
If you're careful about watering you can get them to grow just about as fast, and like you said you don't have to worry about transplanting!
Another consideration is some growers start a lot of plants at once either so they can transport them safely, figure out their gender before moving them into pots, or just store a lot of seedlings at once in a small space without having to use much soil. If you keep a seedling in a solo cup it won't get very big after it grows its first few sets of leaves, so a solo cup also helps keep plants smaller until you're ready to use them.
