Make the 'next page' button in the bottom left have a drop down to toggle it between next page and next spread.
When scrolling through a document now, the view jumps between let and right. It might be less disorientating to switch quickly through the spreads than jumping left and right.
Rainer Klute commented
Of course there are shortcuts, but improving the "next page" button would be a great feature, too.
Or, instead of a drop down, maybe adding a "next spread" button – only showing if you have a document with spreads.
On Windows you can use the Shortcuts:
Ctrl+Alt+0 (Zero) to Center the Spread and
Alt+PageUp/Down to go the next/previous Spread
Hope this helps!