Hello PH,
Absolutely agree about ATHR and TCAS - the imperative is to avoid a mid-air and playing with the TL could detract from the miss distance! Non-precision approaches are an ideal opportunity to fly fully manually from visual or DA so I encourage that but make sure it's understood that ATHR engaged is always an option.
Fully agree about moving thrust levers. A pity it wasn't base option! The non-moving TL rob the pilot of a tactile indication of aircraft performance and therefore degrades instantaneous situation awareness. It makes it more difficult, in my opinion, to effect a smooth "recovery from a windshear recovery". In my experience, the biggest problem people have in this area is not the windshear encounter itself which is usually dealt with well. It's regaining normal flight parameters following recovery from the shear - A FLOOR, TOGA LK, followed by rapidly increasing speed as the shear abates and no idea how to prevent the flap overspeed despite the pre-briefing! Some are not even AWARE of the A-FLOOR/TOGA LK FMA. Often the gear is left down. Its all exacerbated by this reluctance you mention to move the TL from whatever gate they're in. I refer them to the good attitude and power advice contained in the Unreliable Airspeed procedure and advise them to use that as a starting point. And to disconnect ATHR with all haste, control the thrust manually to stabilise speed then select a "known" attitude/power combination e.g. 10 degrees/CLB power then clean up and reselect ATHR on the FCU. Making the standard Go-Around call (not an SOP in these circumstances) serves to prompt a known set of actions and the gear is then not forgotten.
But it really shouldn't be this way.