I pretty much agree with everything here. It's an optional step, but one that I often do (but not always). Depending on the parameters of the mash I often add a boiling water infusion at the end (I can heat the water during the mash, so it doesn't really take extra time) or just run off and boil enough wort to accomplish the same thing.
My main motivation is to increase viscosity and dissolve more sugars (and as an iced tea making southerner who needs to get his tea sweet enough I have a pretty decent grasp of that theory). I haven't ever done any sort of iodine experiment to see if the fermentability profile changed between my first conversion test in the mash tun and the wort in the kettle after runoff, but it would be relatively easy and I'll try it next brewsession.
Note that just because conversion completes doesn't mean the fermentability profile stays the same. After full conversion there is still enzymatic activity (assuming we don't denature the enzymes), primarily resulting in a more fermentable wort. An iodine test can indicate this. IIRC purple/black means starch is still present, reddish mahoganey is converted but not very fermentable, and yellow/no color change is a more fermentable wort.