Two points on that: 1. This would require hardware to be affordable by mere mortals. That hardware is not financially beyond our reach yet, but AI is making the cost of buying good computer parts very expensive. The big corporations are working against the goal of local LLMs in a major way just by soaking up most of the hardware on the market. And I don't even think that's intentional - they're just too hungry to consider otherwise. They can pay high prices where normal people cannot.
2.Local LLMs would have to be designed to be very convenient to use. As it stands, the big players are making their online models very convenient instead, and that let's them charge a subscription. It's a proven business model that our society has gotten used to (even if we grumble a bit). Even if the hardware were cheap, local LLMs are mostly for businesses, with a few hobbyists running it in their basement because they can.
It's extremely hard for me to imagine local LLMs being a threat to the powerful in any way.