Since I work for a company that helps other companies establish their products as well as product organizations, I believe I may have some insight into this. But anyone is welcome to disagree.
TL; DR: your assumption is not wrong if you’re looking at a “narrow” type of specialist and stick to a single industry. Your assumption, however, is not supported by real-world observations and experience, in the case of a “wide” type of product manager who has experience across multiple verticals.
There are still, widely speaking, two distinct types of product managers out there in the wild.
One is a “narrow” specialist, that knows a specific industry, and is really good inside that industry. They could sidestep some of the product methodologies, or may not know the most popular approaches or frameworks, etc. I’ve seen people lacking basic product management knowledge and still working as product managers within their specific domain - because they know “how things work”. These are valuable people and, in fact, SMEs of their respective domains. Eventually, when they figure out there are better ways to build products, than what they currently do, they then become really strong product leaders. And, with a lot of domain-specific knowledge, they become really good at building really good products.
The other ones are “wide” specialists, that may not have a lot of in-depth knowledge about one specific industry. Instead, they have a good command of approaches, frameworks, and overall product mindset that helps them navigate any domain they end up working in. Unless they only spend a month or two within it, they do get a decent level of understanding of the domain. Additionally, by having been exposed to various domains and various kinds of “how things work” across multiple domains, they bring the so-called “out of the box” view almost every time they look at a new problem.
There are others, which are mostly variations of these two in some shape or form. The first one is highly sought after when that one specific industry is on the rise but they can be found wanting during the slump. The second is much more marketable, i.e. it’s usually easier to find a job if you can demonstrate you can build successful products across different industries. The situation is reminiscent of the old saying: “A knowledge of certain principles easily compensates for the lack of knowledge of certain facts”.