Actually for nearly every untrained mind, it's the exact opposite: they can't *stop* thinking (and worrying). Not a sane way to live. To be perfectly able to think and reflect, but *choosing* momentto-moment awareness, this is the way. Thinking has its time and place, but if thoughts run the person, the person is not in control. Thinking then becomes the master - the tool uses the user.
Interesting. I’d say I managed most of my unhealthy overthinking, I tend to think about everything all the time because I’m an analytical person. I like to think. While meditating, it’s not all about absolute stillness, it’s also about getting some important insights (for me). But you got a point, one should learn how to deal with emotions and thoughts!
The insights might be nice - afterwards (unless you're using the word insight as in vipassana, but this does not seem so looking at the context). *During* meditation, they're distractions - just another thought. I like thinking too, but nothing has brought me more peace than not thinking. It's hard to explain. It doesn't make you dumb or simple-minded, although not being *able* to think/reason definitely will imo. It's more about knowing what's truly important - I value tranquility and peace more, and not thinking so much brought more of that. But it's not the absence of thought per se, the absence of thought is a manifestation of the real reason, a cultivation of concentration and insight (in the vipassana sense).
I agree with @papafigos that ALL untrained minds, most all people, are run by unrestrained, automatic thinking. And 99.99% of that thinking is about "Me"! And about the future or the past. And they SUFFER because of it. Being in the present moment, stillness, sensation only, is hard won Beingness. Few experience this. What I might agree with is that, unfortunately, a very high % of those run by thinking, are *wholly unconscious* of that thinking running them!! Making them suffer.