I haven't seen a bench press in a strongman competition with the exception of the incline log press in Lightning Fitness' 2013 Battle of the Thundergods. I doubt I will see another one for a while.
While the bench press is not an event you will likely perform, it is a lift you should be proficient at. The bench press, like it or not, is still one of the best builders of upper body strength and mass that you can perform. And if you want to be strong, you need to get to work.
Of course, we need to excel at all variations of overhead pressing and the bench press is not the primary press exercise in strongman since . And, of course, the best way to excel at overhead pressing is to do lots of it. But bench pressing will give us necessary chest, deltoid and tricep mass and strength to help push out those heavy weights.
For newer trainees, I would focus more on higher volume, high rep training to build mass. Building a solid foundation will go beyond just the extra pressing power, but will also create a bigger shelf to sit your bars on when overhead pressing and provide a big surface to sit other implements on in carrying events if you can hold your carries high. Furthermore, the extra triceps strength you will develop will contribute to your ability to lockout heavy weights if your jerk is not precise.
You don't have to reluctantly go to the flat bench with the Olympic bar to get the benefits, but you can find variations of bench press that are comfortable and advantageous for you. Mike Jenkins liked to use the incline log press and the floor press. Svend Karlsen liked to use the log for incline presses. I prefer to use an axle for bench pressing and floor pressing and switch things up by using dumbbells. Some of my training partners like to use the Swiss bar to mimic the log grip without the limited range of motion the log will create.

Now that you're ready to put the bench press back in your routine, you have a couple of options for where to place it. If you press once a week, I suggest you do it after your main overhead pressing movement. To create balance, I would likely use a different rep scheme from my primary presser. So, if I did log clean and press and was working in the 2-3 rep range I would probably do my bench press for sets of 10. If I was using 10 reps on the log, then I would probably do 4-6 reps on the bench.
If I'm pressing two days a week I would have an overhead press day and a bench press day. This was my favorite split for a while. For example, I would do axle clean and press and dumbbell bench press week 1, log clean and press and axle floor press week 2, and db clean and press with incline press week 3.
So, keep in mind that the bench press does have place in strongman. You will need it to develop your upper body pressing musculature and strength. It will be a good assistance exercise to help your pressing short of practicing the overhead implements. And for those of you with a strong push press or jerk, you might need the added triceps strength to lockout the heaviest lifts.
However, as I conclude, let me state that some of you might already have a base and that the bench press, while excellent as an assistance exercise, might be altogether dropped from your program. This is especially true for powerlifters who are converting to strongman. These trainees will often lack the skills to translate their pressing power from the bench press to the push press/jerk and might benefit from excluding the bench press from their program.
However, as I conclude, let me state that some of you might already have a base and that the bench press, while excellent as an assistance exercise, might be altogether dropped from your program. This is especially true for powerlifters who are converting to strongman. These trainees will often lack the skills to translate their pressing power from the bench press to the push press/jerk and might benefit from excluding the bench press from their program.
If you need more help in programming your lifts for strongman, feel free to contact me through this site or my Facebook page.