My 2 cents; I think the idea that Bench is tricep and upper back is a view which is highly influenced by WSB and just shirted lifting in general.
For me, I used to have a very strong upper back, back and legs. But my Bench was terrible. I actually competed for a couple of years with a awful Bench (200) and pretty decent squat and deadlift (400/500). Predictably at that strength level my legs/back were muscular but my chest/shoulders lagged.
As I finally started putting more and more work into the Bench my entire upper body grew. My chest and shoulders now look pretty big on me.
I think the idea that triceps are important certainly has a lot of merit, I'm not denying that but we need to keep a little perspective here. Just like all of hocus-pocus about squats being all hamstrings. People take a good piece of advice and then just run away with it, forgetting that the quads' primary function is to extend the leg! The chest draws the arms together and it's a large muscle of course it will help, particularly at the bottom.
So let's keep some perspective, especially for a raw lifter sure it's good to train triceps and hamstrings, of course it is. But let's keep not take a good idea and warp it into something else, the chest and quads are still massively important.