I hit a ~300 pound max on the bench press using sets of 8. I literally did 3 sets of 8 (hard sets), training bench about once every 5 days, and opened every chest workout with that same 3x8. These sets were always to failure by the last rep; if I didn’t fail on the last set of 8, I bumped the weight up. I did this same workout every 5 days for a full year. Every few weeks I was putting another 5 pound plate on the bar and it wasn’t long before I hit 300. Eventually I dropped to sets to a 3x5, which pushed me up towards 350 pounds.
I was stuck within 10 pounds of that for a very long time. It wasn’t until I increased the reps that I was able to make progress again. My benched moved from 365 → 405 over the months by using 5/3/1 as the guideline for my first sets and using an even lighter weight than normal. Week 1 I was hitting 12-14 reps; by the 3rd week I usually would hit 8, sometimes 9. I then followed that up with a 3-5x10 with a relatively low load (like 225).
Point is yes, you can make solid progress of strength, even at relatively high levels of strength, without ever using low rep schemes. For me, higher reps was actually optimal, as evidenced by floundering around trying to increase my bench using 1-5 rep schemes for a long time. I’ve always made my fastest progress when working with sets of 8-15 reps. Also, these sets aren’t necessarily “40-60%”; I am not sure where you got that number from. For a working set I recently incline benched 295 for 8, and that was definitely more than 60% of my max.
The thing is when you ask questions like this you have to understand that everyone is different. I originally lowered my rep schemes because perhaps the most muscular person I have ever seen literally said, “If you are doing more than 6 reps on the bench, you aren’t using enough weight”. Apparently that worked great for him, not so much for me.
As far as your original question goes, how important do I think strength is for size? That again depends on your genetics and how well developed your mind muscle connection is with your target body part.
For me, spending years as a kid doing push-ups and cable flies meant when I actually got serious about lifting weights, I had a great mind-muscle connection with my chest. Pushing my bench press up to those levels built up my chest and anterior delts up a significant degree. On the other hand, my training partner pushed his bench up to about 325-335 and did not add on significant chest size; for him he gained most of the muscle in his anterior delts.
On the flip side, pushing my squat/dl strength up did not result in complete leg development… glutes and adductors definitely developed but the quads were severely lacking until I started pushing high rep sets of leg press, using some slower eccentrics, etc. Meanwhile, my same training partner has really put on some mass on his quads after increasing his squat.