I use one of Jaybird's false bottoms in a Bayou Classic 15.5 gallon kettle. Added a home-made dip tube, some valves and a Blichmann Autosparge. I control mash temperatures using a direct fire RIMS with a home built controller running a solenoid controlled valve natural gas. Based the controller design off the Blichmann Tower of Power.
One advantage for me is my mash tun sits right next to my brew kettle on my brew stand. After the stand was built, before I got my mash tun ordered and assembled, I did a few batches with my cooler sitting where the mash tun would go. The heat from the boil kettle burner was not kind to my cooler. It lasted a few batches but I was happy to retire that guy.
I think a kettle mash tun with a full false bottom is helpful for a recirculating stystem. My grain bed just never compacts, even pulling 2 GPM through the mash is not a problem. I put a rotometer on my pump to watch mash flow rates and run 1 GPM during rests and 2 GPM during steps and 0.25 GPM during lautering.
I'm not sure those sort of flow rates are really practical in a cooler. Maybe they are not so necessary in a cooler either. Anyway I do like the bling factor you get with the shiny kettles.