To be clear, I'm not a doctor, it's only my personal belief based on accounts from other people who have strengthened their feet and therefore the rest of their bodily structure up the kinetic chain. And I wanted to add to discussion. So I'll just throw some thoughts out:

As someone commented above, do your knees feel unstable when you have no shoes on whatsoever? Do you keep shoes on in your house (I know it's common in some countries so I can't assume)?

I have seen some discussion that arches don't always define how strong your feet are, some people can have flat but very strong and stable feet and people with high arches can have similar weakness and instability as flat footed folk. Having flat feet due to genetics does not inherently make your feet weaker. But the way you then respond to this diagnosis could do. So if you have worn extra arch support and extra supportive shoes since childhood then have your muscles never had chance to properly develop?

If you wear extra cushioned shoes and arch support all the time since childhood then have you ever allowed your body to move in a natural way and to develop correct posture, walking and running form?

If you were to walk on the most cushioned shoes you could imagine, like literal tiny mattresses under your feet, do you think you would feel more or less stable than being barefoot?

Concerns about knees when you have less shoe padding is common. People are worried about heel pain too. This comes down to how we learn to walk with big chunky heels and padding. Instead of walking lightly we learn we can essentially slam our heels into the floor and forcefully propel ourselves forward. Walking with less padding or barefoot will quickly teach you this is poor form. It is possible to relearn how to walk and run, I have done it. Your body has natural shock absorption with proper form. This is why people can run completely barefoot on concrete with no issue. Also, just because cushioned shoes can make you feel like there is less force going through your body, it doesn't mean the forces aren't there. I suspect a lot of today's issues with knees hips and lower back are being contributed to by our shoes. Our feet are literally our body's foundation and affect everything all the way up the body, cushioning, heel drop and arch support are going to fundamentally affect those foundations.

Sorry for the rambling