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.
That was my point, a liter of jet fuel weighs .803 kg (the constant in their equations not accounting for temp), if you mess that up from the get go, then you are pretty much assured an erroneous calculation.