Compound movements aren't alone going to help your core strength. Infact, I think both go hand in hand. Deadlifts, Overhead Squats, Back Squats, etc depend on you having a strong core. If you train your core to be strong, you'll have a bigger total. There's a reason why coaches like Mike Robertson, Eric Cressey, the Diesel Crew, Louie Simmons, etc focus so much on core training.
It's like that myth that strength trainees don't need to train their arms at all. Well...thats not true. While I do not directly hit arms day in and day out, I think building strong triceps are good. Same goes with biceps. Everything should be trained. And Core strength is probably one of the most important aspects of strength training. You're only as strong as your core at the end of the day.