Would it hurt the engine or transmission to skip shift from 1 to 4 gear.
I just did it and you see a big increase in mpg about 4 to 5 to be exact.
I know some GM cars like the corvette and camaro have them to avoid the gas tax.
Drive slow enough and the trans will do it for you already, via the skip-shift solenoid. Short answer is no, you can select any gear you want, in any order you want. I often go 1-3-5 on my 3.73 car around town.
I don't ever get forced into the 1-4 skip on my '13. I do the 1-3-5 skip myself when putting around town. I think if anything that helps reduce wear since I'm rowing less--both on the trans and my clutch leg.