The quality of a product is not like wine. It is not improving with the years by simply letting it be. On the contrary, it needs constant maintenance, even just for keeping it at the same level as it was before.
Changes to its surrounding environment or ecosystem, whether it is browsers, operating systems, consumer devices, HW, formats, security threats or anything else, create the reality that there is no such thing as 'last-forever product'.
In a broader perspective, the cost of maintenance throughout the product's life-cycle is usually higher than the cost of the one-time, first product development itself.
In my past I was part of a QA team, doing my fair share of testing, which never actually stopped even while managing product design and delivery. Along the years I realized that good QA managers exist but hard to find, especially compared to other managers in tangent domains (SW development for example).
I've also learned that when it comes to testing and owning the quality of the product, the secret-sauce is in the people doing the work and not with the method it is done. Methodology is important (and I will leave that discussion to real QA experts) but the psychology is the starting point in my mind.
There are some fundamentals that should be rooted in the tester (whoever she is, not just in the QA team), where as the methodology can help to perfect the outcome but not replace them.
QA is bold! It is the gate-keeper of the product. It is the last piece of the chain before the product meets the "real world" and real customers. There for, it is meant for someone that can speak up and speak loud. Even if the methodology provides the tester the stage to report the findings, to recommend or even decide, the boldness is to make sure the right decisions will be made and the statements will echo all over.
It is not at all about finding bugs, it is about finding the RIGHT bugs. Sometimes finding JUST bugs even harm the quality of the product because these non-important bugs will mask the important ones, and will focus everyone to the wrong place. There is no equality in quality!
What are the right bugs? The ones that users are most likely to face. Testers needs to learn, understand and adopt the users' way of thinking and operating, in order to succeed. The ability for one to look at the world from another's eyes, Empathy, is an important pillar of the greater product team and that is a fact in any testing methodology.
Quality is an on-going process and there are no short cuts. That is fundamental, not just for the testers to understand but for any participant in the product development cycle. Methodologies can provide guidance to to re-test, repeat, compare, but that something inside will provide the drive to reach that desired level of quality. Perseverance or even grit is the attribute to look for.
Quality is mostly a team effort, much more than other aspects of the product development process. It is not a task or a burden on a single person's shoulders or even a specific group. This accountability for quality is a state-of-mind that all participants should have.