Unit cancellation won’t help you out much if you start off with an incorrect constant. The speed of light is 2.99 x 10’8 m/s, if you think it is 6.0 x 10’8 then I don’t care what you do, you’re going to come up with an answer that is way off.
If you use units on your conversion factors, you don’t use the wrong conversion factor. People don’t make up constants. THey look them up and use the wrong one with the wrong units. Or if they write them down in a notebook without the units at all, they don’t know when to use that number and when not to.
Unit cancellation works. It would’ve prevented the mistake in the fuel calcs. If you are so stupid that you make numbers up, then no, units wont help you. Nothing will.