Why did the Senate stick around?

Based on the movies alone (from your comment about not wanting to include other Star Wars works)

We are not given a great deal to go on apart from the fact that the Galactic Republic seems to have its power vested in a Senate of officials from planets in the Republic and special interest groups like the Trade Federation. This Senate then elected a Chancellor who is the leader of the Republic and Head of Government.

It seems likely that given the vast size of the Republic, that this form of government has existed for a long time and therefore the mechanisms and institutions of governing the Republic are used to reporting to the Chancellor and Senate.

It seems it might just have taken 20 years of slow change from the Senate/Chancellor system to direct rule of the Emperor via the Regional Governors mentioned in 'A New Hope'. One can surmise from the 'last remnants' comment, that this was a final step and perhaps the Senate had very little power at this stage. Why did the Emperor do it this way? Perhaps he surmised that a more dramatic change would be harder to manage and more risky than slow inevitable takeover. Palpatine seems to work mostly by deceit and corruption rather than outright aggression.