As for siniwali being used in actual combat historically, I do not know. However, it is a good drill to use to build coordination in both hands. One can never guarantee what will transpire in actual combat.
You can't guarantee which hand the stick will end up in- you can't guarantee your "good" arm/hand etc. will be able to hold a stick, or anything else for that matter, so it behooves one to learn to use both hands.
As for sticks being out in the world- funny you should mention this. I was talking to a training partner the other day about this. If you look around, they are present quite often. Some examples-
I was in the gym, and noticed various barbells without weights on them, and then handles for various machines, like the lat pulldown bar, and the tricep extension bar just laying on the floor near the machines.
On the street, I've seen 2X4's, lengths of rebar, broom/mop handles, rakes, shovels, pipes, fence posts, various signs stuck in the ground, pieces of furniture, and the list goes on. This isn't pie in the sky either- these are things I see often.
Inside in various places, like restaurants, nightclubs, schools, and other businesses, you'll see- pool cues, mops, brooms, signposts, various poles used to hold up velvet ropes or chains, handrails, chair and table legs, and the list goes on. Don't forget, things can get smashed/broken during a fight, and then things you never thought of could become available, especially during a riot/brawl. Why not use them if it's appropriate? Hell, break a chair or something if your life depends on it. Especially break it on the opponent!
Don't tell me there are no sticks around. There are objects everywhere if you really look.