I think that compound free weights are very useful even to a high level diver. Having said that I would do them mostly in the early (foundational) training phase, and decrease them to one session per week in the transition phase and eliminate them in the final 6 weeks of the competition phase.
That is pretty much exactly how I've included strength training to my training program. I've been doing deep squats, deadlifts, bench presses, barbell rows and some additional exercises for 5x5 reps. My idea has been to accumulate necessary base strength without acquiring too much muscle mass and 5x5 is good for that.
Since most of the time I'm having only one or two strength trainings per week, sometimes none, my results are modest, with 140 kg deadlift, 125 kg squat and 75 kg bench press (@ 183 cm, 73 kg). During the last two months my training has been only diving and I've clearly lost lots of muscle. Not that I had it that much in the first place, but still. After I'll retrieve my former travesties of muscles I will just keep the results there or slowly brush them up since I don't think additional pure strength will help me that much with freediving.
Instead, in the near future I'll try doing some longer series to train lactic acid production and muscle endurance, series like 3x20-30, an aspect I hypothesise to directly help my DYN/DNF results. I could be wrong here, but with my knowledge I think it would be best for freedivers to usually avoid doing 3 x 8-12 rep style training, because it causes more hypertrophy but still not lactic acid endurance. I'm with efattah with the fact that free weight (barbell) training is usually much better than machines since they train more muscles at once and you have to balance the weights yourself.
About the general usefulness of strength training for freediving, I would say it's an important part of a balanced training schedule. I don't think freediving is much different from other sports in this aspect. Sport-specific training will only get you so far, at some point it's always more efficient to add different kind of training to your program. For example, javelin throw is only about who can throw the javelin farthest. If you're a beginner, at first your results will get better by just doing specific training and learning the right technique of throwing. Keep training that way and your results will still grow, but slower, as you are just training sport specific muscles. However, after that you will stall, sooner or later, and you will also get other problems, like shoulder injuries and so on. It becomes much more effective (and healthy) to add weight lifting, sprinting and other things to your training instead of just more javeling throwing.
Specific training is the most important sector of your training but it should not be the only one. In freediving you move by using your muscles so it should be clear that better trained muscles do the same work more effectively. On the other hand, of course, too much (or wrong kind) of muscle training and muscle mass will disturb your actual training and impair your results. However, balancing the different sectors well will get you better results than you could ever get by focusing only on one sector. Thus, it should be no surprise that former competitive swimmers like Frédéric Sessa or Dajana Zoretić have quickly risen to the top of the competitive freediving world with quite a short time of actual apnea training. They already had their other sectors of training in good shape.
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