I had a few thoughts after reading some of the replies.

1.) Most garbage disposal manufacturers warn against shoving piles of
peelings down the disposal, so it makes sense to peel into something
you can empty into the garbage or a compost pile.

2.) Even if you decide to peel into the sink, who cares if peels get
soapy, or get pasta water on them? It's garbage. You really don't do
"food prep" on the dirty bottom of a sink.

3.) When someone needs to drain a big pot of boiling pasta water,
you're going to get out of their way anyway, and it takes mere seconds,
so a divider isn't needed.

4.) If you feel you need to soak some dish, most items (pots, pans,
plates, casserole dishes, etc) will hold thier own soapy water, so
there's no need for immersion. And without a divider, there's more
room to set set dishes.

After two years of putting up with two basins, I realized one day that
not once in all that time did my wife or I ever need or use that
divider that was getting in the way and taking up valuable sink room.