If the new ones are doing PWM (I hadn't heard that's how it works, but have no reason to doubt it), it must be cycling several times per second. It's indistinguishable from having true control over the wattage.
The old cycling on and off, it's full power for several seconds and then off for several. The full power sections are long enough to nuke the shit out of many items. Butter doesn't do well, soup and pizza either, just to name some.
I didn't realize PWM specifically referred to fast cycling. I thought any sort of deliberate on/off pattern to modulate power would be PWM. What you said makes sense though, that the regular microwaves can't lower their power output enough (whatever The mechanism) to be safe for some foods.
