The form you use is part of expression.
Engagement maximizing is a buzzword that translates to content people are interested in viewing. Why would you want to regulate content to be uninteresting? I can't see that benefiting anyone.
Who decides what makes an algorithm engagement maximizing instead of you know, user satisfaction maximizing (because satisfied users stay around for longer, right?)
And who decides what is extremist and what is acceptable? Was Rush Limbaugh reading the names of patients who died of AIDS on a hundred year old media more or less extreme than someone praising mao zedong for killing all landlords on social media?
Let the user decide. The evil algorithms require the "algorithms" such as "all my subscriptions, completely, in chronological order" to be removed. If "all ragebait" or "maximize profits for facebook" are just other buttons, I have no objection, but I do not think they will be popular.
Not if you must ID before accessing information on the world wide web.