I think your argument depends, one what capitalist societies we are talking about.
When it comes to access to education, then most capitalist-liberal-societies have managed to create a system of education that is theoretically open to anyone, for pursuing any career option they deem fit for themselves. If we were to look at the case of the United States, or countries where such an "open" system of education does not exist, the problem generally gains a financial dimension and your argument would be, I think, very true. But anywhere else in the West of the World it is, in my opinion, a bit more complicated.
In that sense, philosophy and science, become only differentiable through the means necessary for each, to come to results. In science you are only able to come up with results, and prove them worthy of being called "truth", by making use of infrastructure that is hard and expensive to come by. But if we locate the argument, within such an "open" system, as I described it above, one is perfectly able to make scientific innovations with the help of public funding or within the frameworks of larger corporations or government institutions. Actually, rather few of the worlds scientists would be considered "rich".

Speech controls us as well. To state otherwise is, I think, an underestimation of the power of speech.
If we think of the prague structuralism and/or Ferdinand de Saussure, we learn, that
human beings conceive their world partly through language. In fact, one of the primary functions of
speech, in linguistics, is the cognitive function, which enables us to think and formulate our thoughts more clearly and precisely.
One must not forget, that any revolution, for better or for worse has started with an idea or ideology that was delivered by speech.
It is right, that no word can make a feather move, but it can move hearts and minds within the realm of human social interaction. And the notion of something like "incitement" heavily or rather fully concerns the "human
realm".

The true agents within human interaction, I would argue, are our minds, which are almost entirely influenced by outside values brought into them. Words cannot make a feather move, but a touched heart and a well instructed (through speech) mind, will makeit fly in no time. (Of course, outside of the metaphor, almost anybody is able to make it fly, but let`s say, for the sake of the argument)

Concerning the actual point of discussion, there seems to be a problem of quantifying what harm an opinion is able to cause, within the political-societal framework, and at which point the regulatory institution ought to intervene. I think in order to be able to discuss the problem properly, one would have to define the dimensions of "incitement". Mill himself was, though advocating freedom of speech rather profoundly, against incitement or "spoiling the youth". He just might define those terms differently
to you.

I propose, that preventing a man from speaking to a crowd with hay forks and torches in front of the mayors house about the recent misconduct of the mayor (almost exactly Mills example) is no threat to public discourse. I would say, incitement begins, where violent action might be expected as the direct result of speech. Of course, this is the extreme end of incitement, and the other end still needs to be defined.