This is interesting, having been teaching steep turns this morning, my mind's fresh.
I can absolutely see Whopity's viewpoint that a steep turn is an avoidance manoeuvre, without pause or checks. That would appear to match Pull What's "collision avoidance" turns, and for that matter how I think of the manoeuvre and both practice and teach it.
But the 360deg turn - what's that for? A co-ordination exercise? A primer for aerobatics one day? Demonstration of situational awareness? Setting up for teaching about spiral dive and recovery? I can see it has value for all of those: and hopefully most good instructors use it for most of those reasons - but does that require HASELL checks in any case? You're not going into negative g, you're not going near any mode that's likely to cause a loss of control. If it's flown faintly in balance, nothing that's in the aeroplane should shift. The engine is not being asked to do anything special. On the other hand, getting pilots into the habit of doing HASELL checks before a steep turn might create a "bad habit" pause when they need to do a steep turn for safety.
So why HASELL checks? Yes before stalling, but steep turns? Can't see the argument.
G