Add Busan when the group wants enough time for it, not merely because the train makes it reachable. A KTX day includes checkout, station access, luggage, arrival and a second hotel; leave that date light.
One Seoul base preserves the open blocks
Seoul-only gives you more freedom to change the day, return to the same room and keep dinner near the hotel. It can be the better fit when flights already shorten the first and last dates, or when the group wants fewer luggage moves.
What a Busan week asks you to give up
Choose two consecutive Busan nights only if the coast, port or another specific area is on the group’s list. Place the KTX between full sightseeing days, and keep the first evening near the new hotel. Do not plan a long cross-city outing immediately after arrival.
Choose the train station with the Seoul base
KTX and SRT use different Seoul stations. Check the live schedule, departure station and arrival time before choosing the hotel nights. A schedule that looks short on the train can still require a long station transfer and a slower return to the room.
For a split trip, arrange the order around the actual arrival and departure airports. If the Busan segment leaves only one rushed day, use those nights to give Seoul another full day instead.