Kakao Taxi is a bad option for foreign visitors. It is a hassle to set up if you aren't already part of the Kakao ecosystem, and if you don't have a Korean bank account or credit card, you are limited to regular taxis (which you have to pay in vehicle), and the supply is limited. I had zero luck on multiple occasions trying to get a large vehicle for a group of 5.

TADA works with foreign cards and is much easier to set up. Uber is also an option in Seoul, but only offers sedan-type taxis (max capacity 4).

A more minor annoyance is that Kakao and TADA both suffer from incomplete English translation, and frequently spit out Korean-language messages even if your phone is set to English. As a non-Korean speaker, I would be tempted to stick with Uber in Seoul for that reason alone.