It’s still going to be far more accurate than the random scale on the swinging arm, once you achieve the correct tension double check with a laser line to confirm. So you should now have your measurements with any deviations. It’s never failed me in over 25 years. What does amaze me is the amount of run out in the tolerances of aftermarket sprockets, I recently had to return a brand new Talon sprocket for this very reason. Poor quality control. By all means use the lines for initial setup and then use a vernier for the final micro adjustment.
I use my vernier to measure both sides as others do. Then I get the laser out, mount it on my tripod and check alignment.
I use string lines for checking wheels, same idea as Mark, it is probably more important your wheels are in line rather than the chain, but ideally both. you can check your car wheels as well this way
I'm not sure that laser check works. Isn't the idea to check that the chain is in line with the rear sprocket? The chain could still be in line if the sprocket is at a slight angle to the chain. The lasers designed to check chain alignment sit on the sprocket and you follow the laser line down the chain. I've never tried your method though, so I might be wrong.
I use the slightly older version of this, very handy and agree needs to be aligned off of sprocket to ensure chain is straight