That's about the size of it. They certainly can be used to improve a system - they just generally are used for other purposes. Likely all of the purposes that people suspect are somewhat true: They're used to test for potential backlash and to build hype, more than to improve the game (though I am sure that improvement is never not a part of the goal - it's just not a primary one).Yes if done right.
"Done right" means having the system pretty much nailed down before releasing to open playtest, and using the open playtest almost exclusively to find and fix errors, omissions, bugs, glitches, and unforeseen rules interactions.
do I really think someone reads through and analyzes tens of thousands of feedback forms?
How to do market research has not been forgotten the methods are still there is the literature. It is not compatible with the investor classes aims to do quality products in many consumer sectors but to get into the details would involve some political analysis.No, but dating back to the 1950s, properly written market research surveys with imposed structured data, could be analyzed.
That fact that mankind has lost both the knowledge and will to do market research the right way, kind of explains why most products are so terrible now.
This is a question about public playtests specifically.It depends a bit on your design intent. If you're making something for your own pleasure without much consideration for potential players, customers, then it's probably not really required. It definitely helps to iron out details and bugs. But that's something you can do on your own over time by playing it.
Otherwise? Playtests are absolutely invaluable.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.