Back in the day I worked for the Navy as a contractor. The first company I worked for was absolutely professional. They never hired anyone above you that didn't at least have the training to be there. They might not be competent, but at least somebody invested the time to train them.
The second company was a $#!+-show. They'd hire anybody off the streets to be your supervisor - and then pay them less than they were paying you. They're attitude was that the person would sink or swim and they could underpay them until the person performed. They lost the contract at the first opportunity - but I'd already decided I didn't want their stink on me and I'd left. They hemorrhaged talent.
The training matters, but so does the competency. With that certificate you stand a better chance of working with someone who at least has a clue. With the second company, we peons were getting really tired of training our leadership how to do their job.
ASE itself was always a self-serving cash grab. They moved from technician testing to jumping into certifying everyone they could find. Parts guys were getting ASE certifications. I believe ASE tests have their place, but technician training has evaporated. Too much of working on cars has moved away from understanding the physics to knowing the stupid tricks the auto makers make you jump through to wrench on their specific cars. Now we have mechanics who can't think through the physics of why a transmission rumble goes away when you push in the clutch pedal. Electrical troubleshooting especially has become a lost art.
Customers don't care about ASE certifications any more. Too many shops have ripped customers off while hanging that ASE shingle on their wall. Nobody gives a f***.
I had four ASEs, but I didn't get paid any more for having them. I was judged more on my ability to look at a car and magically know what was wrong with it, and then cover my @$$ with bs when wrong.