Not true. MAUW, g-limits, Va, Vs etc. are all interconnected, but related to the aircraft's design spec. Modify one, and it has a knock-on effect on all of them. This is true of any aeroplane, but a peculiarity of civil light aeroplanes is that there are max/min values which must be met (Vs and g-limits in particular).
I've come across a few aeroplanes where LDR/TODR are considerations also, but very few and none of them were common light aircraft.
As for insurance - try asking your insurance company how they'd feel about it!
G