your website gives the preliminary list.
That is an excellent point. :)
Keyword data associated with how people are currently reaching your site is important, very important. I think this data is underutlized. It's a rich source of information. As noted by the member I quoted, it's a preliminary data source but an important one. It's preliminary because the data is limited to what you know (and what you think you know).
An important aspect of keyword research, the next step after you've exhausted the preliminary step, is finding out what you don't know. Things like how the crowds think of your product/service/app, what their expectations are, alternate ways of using it, alternate ways of searching for it, etc.
An example of alternate ways of using a product could be found in matzo meal. A matzo meal company may think of their product as for making matzo balls, but a significant amount of their customers may be buying the product for fish fry batter. This is actually a common (and unintended) use for matzo meal. Keyword research would uncover this kind of thing.
Companies can get locked into a certain way of referencing their products. I did a site review at PubCon where the company had a specific descriptive phrase, Widget Information (for example), in their title tag. I researched the keywords while my co-panelists were talking about other issues and discovered a flaw. So I asked the company representative what the site offers. The company representative responded that the site gives Widget Advice (not Widget Information as is posted in their title tag). I then pointed out that according to several keyword tools, Widget Advice has almost double the traffic. I asked him to confirm if this is true and he affirmed my observation.
That company had been locked into seeing themselves as information providers. But their site visitors were coming to their site for advice, not for information. There's an important distinction between the two. Advice implies guidance and authority. Widget Advice also offered more traffic that was also more relevant.
Many years ago I worked for a company that had one of those compound names, like ExampleWidget. What I discovered was that about 40% of their potential clients were searching for Example Widget and they didn't rank for that phrase, their reseller partners did.
An important aspect of keyword research is discovering how they
think of your products/services/etc. It can get granular and longtail.