Weight and Balance is a whole different ballgame!
What you say is true however there is a reg which says to follow the AFM hence the loading system in there. Some aeroplanes have a loading system approved by a Weight Control Officer which is different from the AFM - and that loading system is not part of the approved AFM.
Regardless, no law mandating how you do the arithmetic - whether you use a spreadsheet or mental arithmetic or an EFB then its OK - you take responsibility for the arithmetic.