just a few words - I don't "challenge" Mr. Papi and if I ever get the chance I'd be curious to hear his take about a more specific question in that matter.
To my personal experience a fillister type screw might be easier to be polished to a certain degree - and a flat head might be harder
to polish in the first step, as it easier shows the imperfections an tiny scratches.
If done to a higher degree of finish - personally I've found it easier to get, let's say 5 matching flat head screws to a good level compared
to the same number of rounded head screws. Supposed one tries to achieve an equally good finish.
If that's the "challenging" you mean - I'd call it more a minor disagreement - but I'd not be surprised if in fact there isn't at all .
Besides that, the only thing Mr. Papi indeed says about Fillister head screws "they're uncommon in upscale horology " nowadays....and in another place he
admits they're "esthetically pleasing" - .that doesn't sound negative in the way you do suggest? Another quote he groups them together with the flat head screws as
the ones to use...?
Throwing extremely cheap unfinished screws in the same basket - and dismissing fillister head screws for the reason "they could confuse consumers" , sorry Bernard......:-(
BTW, the "slipping screw dirver" - there you're confusing me a bit. In high horology, or let's say in good watchmaking - a damaged screw is
replaced or reworked/polished - if on the outer circumgerence or the entire head - I don't see the difference. And under normal circumstances, the issue is either the bridge/plate is damaged due to the "slip" or the slot is "lipped" - which indeed is more easy with non bevelled slots - but the same when the slot is acurately finished.
Both surface geometries do have their difficulties, but IMHO there's little difference, if at all when done to the same degree.
BTW, if I'm not mistaken - you're also quoting my words incorrectly.
Best regards
Suitbert