The company I work for has standard load plans that mean we do not have to plot CofG if we load in accordance. (We just write "SLP" through the trim sheet) Sounds much the same as your previous operator but on small turbo props.
From my experience as a dispatcher - Most airlines have standard load plans but it does not normally exempt them from doing a CofG or trim calculation. I have only seen the exemption from CofG calculation on smaller aircraft where take off trim setting is estimated rather than calculated. The largest aircraft I have seen the trim sheet "SLP'd" is an ATR 42.
Ryanair use standard load plans along with a cunning system of trim calculation that works by having a standard trim effect added to standard weights as a decimal thus the last Kg and decimal is the total trim effect of the load. I think this system is very clever and have not seen it used anywhere else.
Hope this helps