Most radical shifts, especially as large as revamping an entire economic system, were violent or at least highly outside the existing framework, not some "change from the inside".
Behind any government is a desire for self-preservation - and capitalist democracies rig elections by underrepresenting the disadvantaged and also, as other systems, through the bureaucratic inertia that is there for a reason.
Taking America as the most studied case, the two-party system absolutely does not allow for the building of socialism, as both parties are highly capitalist in nature, and the rest exist there as a pure formality, deprived of resources for actual political campaigning. All while plenty of anti-freedom acts are taken specifically to silence who people in power don't want to see.
At the same time, the two leading parties create an illusion that this is the only choice and that Democrats are "the left" and act in the interest of the people. Even the most unprecedented case - the campaign of Bernie Sanders - came with what essentially can be seen as centrism - and even that was seen as "too much" with him failing miserably.
Similar story in many countries.
They flood the media, they control the opposition, and they approve anti-democratic laws - all to cement their place and make sure exactly that no change is ever gonna come from the inside.
Which is why, sadly, through all my desire for peace, I have to say that small and steady change is not enough. That's not to say that you shouldn't vote whoever's the biggest and leftest in your area, that you shouldn't do what is within the law and the current system to improve the situation where possible - but thinking it would be enough is a bit of a fairy dream.