If we keep eating our own, others will eat our lunch.

[Bluenorthwest]

4. I would say people in the center can and do the exact same thing.

Trying to persuade a coalition to support your point of view is what everyone in politics does. Everyone. Those who behave destructively when they fail to do so are people who are making a choice and they come from all places on the political spectrum. It was not liberals who marched off and voted for fucking Ronald Reagan and called themselves 'Reagan Democrats'. Nothing says 'undermine the Party' like voting for the opposition. So many did that. Know any? I can name some among current Democratic 'leadership' who did so.
On the other hand ideas that are 'at the edges' do often become the ideas of the majority coalition, providing forward momentum and a renewal of ideas.
I mean, I remember when marriage equality was a position held 'by people on the edges' only. Hotly resisted by the Center and the Right.
It's politics. And you can look at the Tea Party if you want. I'll look at the constant progress my communities have made in spite of fearful centrists and hateful conservatives. This country is moving to the left, get used to it and don't mistake the weather for the climate.