Based on personal experience, it is practical to just show up at Seoul Station during the week and buy a ticket for a KTX train on the spot. If all of the seats have been reserved, there are standing tickets available, too.
Based on your earlier question where you would prefer the option of a non-reserved/standing ticket to save 7400 KRW (US$/€5.50 or so), perhaps the prospect of potentially standing for a couple of hours does not concern you.
However, for the benefit of others, my wife and I once endured a standing journey from Seoul to Busan — purchased at the station on a whim for a midweek jaunt during the summer — and the experience encouraged us to always book tickets in advance for future train travel in South Korea. Busan is a very popular summertime destination, though. Your odds of a seat likely would be better on a random weekday in October.
Trains often do get fully booked on the weekends and on holidays and there is a limit to the number of standing tickets offered, as well. For example, Korail reported that 48.3% of tickets were reserved for Chuseok (Mid-Autumn Festival) this year on the first day they went on sale (30 days in advance).
If you want to travel on the weekend, a holiday, or there is a special event/festival, etc, it would be wise to book a ticket in advance.