I don't think it's that simple. For one thing, AI isn't a democratizing force. If it's as good as you think it will be, it will be less like having a good education and more like having an indentured servant. Some people will have whole fleets of such servants doing their bidding, while others will have none.
For another, research isn't an end unto itself. As you note, for some people an already-unfathomable level of societal knowledge has resulted in nothing but continued poverty. Benefit from scientific knowledge requires a stable economy full of consumers who can and will purchase high-tech items. Where will that wealth come from once the value of human intellectual labor has been so undercut by cheap AI intellectual labor? Without the capitol to make AIs work for us, most if not many people will be left to live their life as servants to AIs so that those AIs are able to have autonomy in the real world.
For another, research isn't an end unto itself. As you note, for some people an already-unfathomable level of societal knowledge has resulted in nothing but continued poverty. Benefit from scientific knowledge requires a stable economy full of consumers who can and will purchase high-tech items. Where will that wealth come from once the value of human intellectual labor has been so undercut by cheap AI intellectual labor? Without the capitol to make AIs work for us, most if not many people will be left to live their life as servants to AIs so that those AIs are able to have autonomy in the real world.