If you're welding 1/4" or greater then changing waveforms may not make a dramatic difference visually, unless you choose the Triangular form which is for thin material then you may struggle to form the puddle. If your welding very thin material then you'd see a greater impact from the different forms. Bottom line I believe it's a useful tool to achieve the end result.
Example, if you have 1/2" plate you'll want the advanced squarewave, AC balance to EN, and also preheat to help make a successful weld, if you have a dynasty (or other inverter) that allows independent amplitude adjustment then that too becomes another tool that can be used. For many years before inverters, successful welds were made on aluminum using just sine wave, so you may not notice a dramatic difference by changing the wave form, but it is adding (or not) to the heat input.
If you were to inspect two finished welds, one made with all the inverter tech and one made with a transformer machine (assuming both welds are done properly) you may not be able tell which one was made with the inverter*, but the welder may say they appreciate having the advanced tools to work with.
*Under some circumstances you may be able to tell, such as narrow oxide etching due to the inverter settings
To avoid criticism, do nothing, say nothing, be nothing...sounds boring to me