Gary, the burner drawer mechanism is very sturdy! Trust me, I had to figure out how to get mine apart and back together again... The base cabinet is pretty darn heavy, too. So far, nearly 3 years into using one as the 'daily driver' at the house in St-Lib and there have been no tip-overs or other disasters when using all 4 burners.
The issue I immediately spotted, however, is if you have a cabinet above the stove; trying to reach into such a cupboard (if you can even do it, I'm too short...) could result in a nasty spill or burn.