There isn't an uproar (except among right-wing activists) because these companies only control the flow of information on their own platforms, not across society at large. Literally every platform and publisher in human history not directly controlled by an authoritarian state has had the power to decide what they will and will not accept, and every site on the internet that accepts user submitted content does so under terms of service which likely allow them to be able to remove any content they want at any time for any reason.
And prior to the internet, fewer media companies than the number of streaming hosts and social media sites that currently exist had much greater control over the flow of information in general terms than Youtube does now.