Could there be an option to click, drag and pull, skills on the sheet, to make that bit a bit more user friendly. You can already make new skills so why not be able move them around.

There is nothing wrong with the alphabetical order, maybe they could they be arranged for example by the ability they use ? 

If you would the ability to fiddle your skills around Would you ?

I am completely indifferent to this idea, but I am going to vote no for the sake of consistency between different versions of character sheets.

Would love to have the skills organized by category!
For example, it's so much easier to find a charisma based skill when it's under the charisma category.

Quote from keecho >>

Would love to have the skills organized by category!
For example, it's so much easier to find a charisma based skill when it's under the charisma category.

 Skills are only loosely tied to ability (you might make a strength intimidate check to intimidate with your muscles rather than words for example) so it makes sense to list them alphabetically so you can find them easier.

Having them listed alphabetically also helps if you don't know what ability a skill is normally when the DM asks for a check.