edit: Whoops! Shouldn't have revealed I'm a Bernie supporter. Forgot that HN is a libertarian paradise!
It's funny, some threads you'd think everyone here was at least a socialist. Then in others you'd think everyone is one step short of declaring themselves sovereign citizens.
I think the lizard people who run the site just flip a coin when each story is posted to decide which kind of comments it'll have.
Electing Bernie won't make a huge difference if the republicans still control congress.
Your idea seems to be more of an observation of recent presidents than a property of the presidency itself. I think there are two things that make it so. First, modern presidents are generally picked from a very narrow pool of candidates which the parties and the media help select and shape, thus making sure a relatively docile candidate is chosen. Second, most modern presidents are very politically oriented and beholden to the groups that donated to them during their campaigns.
I think that can be used to describe Hillary, but I think both Sanders and Trump are non-docile and not beholden to outside interests. Sanders, because his funds largely come as a mandate from individuals and he is very clear about who he works for. Trump, because he has nothing at all to lose by doing whatever he wants.
Would that be illegal? Would it be speech? It's not like the President would be telling you who to vote for (though it might be different if the US had referendums, because the President would be telling you what to vote for); the President is simply attempting to sway your opinion, and then telling you to inform someone else of your (hopefully swayed) opinion.
However, even if democrats won back the majority of congress -- are there enough left leaning democrats enough to support Bernie's platform?
Consider, for example, a Sanders DOJ vs. a Trump DOJ? (I suspect a Trump FBI would be primarily interested in cataloging and spying on anyone critical of Trump or of Muslim faith, essentially use COINTELPRO as a starting point, but make it better and stronger and do good deals). What about a Sanders DEA? EPA? DHS? The executive can do nearly anything if they are bold enough. The executive can ignore the judicial branch ("He has made his ruling, now let him enforce it"), the legislative branch (subpoenas from congress? About illegal leaks of classified information for political purposes concerning Valerie Plame? Please direct the law enforcement officers with weapons in your branch to serve them. You don't have any?)
I believe Sanders would refrain from using executive power to make things worse, while I am certain all of the other candidates would not refrain. Hillary will not differ from Obama nor does she claim to. Trump's shtick is to be an American dictator, an executive strong man who advocates violence and abuse towards anyone who disagrees with him and acts as an outlet for racism and hate and anger. Imagine if he had an army of FBI, DHS, NSA agents at his beck and call.