As M.B. says, there are many times when it is not possible to substitute a 6 jaw for a 3 jaw.
Sometimes a 6 jaw is just the thing. My second ever lathe project, 25 years ago, was adapting ABS to my race car and I had to substantially enlarge the spoked bore of powdered metal reluctor rings. I was very fortunate to have access to a well tooled HLV-H in the Do-It-Yourself machine shop at work, and used an available 6 jaw. By "have access", I mean it was always unlocked and there was no sign that said "Glug, Keep out!"
It was important to not distort the rings with the jaws, and not have the work piece slip during the interrupted cut. To make it more challenging, in my inexperience I started the large bore as a facing operation into the spokes rather than remove the majority of the material using a more appropriate method (hole saw would have been fine). As soon as I set this up I saw how lousy the tool geometry was. I took it slow, got lucky, and had a good outcome. I'm sure the soft material helped a lot, but also made distortion or failure a substantial risk.
If you pay attention at auctions, you can strike gold by finding a full range of pie jaws for a song. Obviously it helps to get the matched chuck. I got 4 hardinge air chuck setups and jaws that way, for about $100.
Obviously the adjust-tru won't allow you to adjust the jaws individually, though they do make independent 6 jaw chucks.
A couple years ago I scored a nice 12" 6 jaw adjust tru Buck, with an L1 back and 1300 rpm limit, for around $125. The price when new in 1966 was $562. In 2020 dollars (pre Corona!) that's $4487.