Roll vs. Role, 5e vs. Old-School

I've been playing 5th edition D&D  (5e) in a face-to-face game for a
few months,  which, for me,  has really cemented the  divide between
roll vs. role-playing and player vs. PC skill.

[My  one-and-only exposure  to 5e  before this  was at  a convention
during the  D&D Next  playtest period][1], about  six years  ago. So
even though my memory is hazy,  I don't recall thinking that we were
rolling skill  checks all the  time. Maybe it  is the DM  (and maybe
other 5e DMs can chime in here),  but nearly everything we do in the
5e game  is based  on a  roll, tied  to some  stat on  our character
sheet. We  roll **constantly**.  "I search the  sack... OK,  roll an
investigation  check"  or, "I  examine  the  fireplace, looking  for
cracks or anything irregular about  the stone floor and sides... OK,
roll an investigation check" or "We move down the hallway, trying to
be quiet... OK, roll a stealth check". So the [old-school primer][2]
is  accurate  in that  regard,  and  I  find it  distracting  during
play. We're constantly  looking at our character sheets  to see what
it is  we can  do in  any given  situation. It  also seems  that the
player is making most of the rolls - which is fine sometimes, but in
a lot  of cases this  encourages meta-gaming when the  other players
see a poor roll and want to  try the search or listening at the door
or whatever it is themselves.

I  also notice  the  power  creep. My  2nd-level  Druid can  already
shapeshift into animal  form, and has three cantrips he  can cast at
will, one of which is the well-known _Shillelagh_, which gives him a
magic staff with +5 to-hit and  damage (his spell attack bonus) that
lasts for  10 combat rounds.  Our 2nd-level Ranger can  already cast
spells and has +6 to  stealth checks. Our Warlock can telepathically
communicate  with  any  creature  within  30',  regardless  of  what
language they speak, and has  the _Poison Spray_ cantrip, which does
1d12 damage on  a failed save (I mentioned the  powerful cantrips in
my [convention report][1], so that at  least did not change from the
playtest).

All that said, the combats are fun  - 5e combat does not seem overly
complex  or slow,  although there  is not  the ever-present  fear of
death that pervades old-school games. It is very easy to regain lost
hit points, and  the multiple saves versus death mean  PC death must
be  pretty  rare (it  hasn't  happened  to  us  yet). And  with  the
aforementioned power  creep, we're doing significant  damage on each
attack round. Finally,  with its reliance on character  skill, 5e is
far  more forgiving  of  bad  play and  tactical  mistakes than  the
old-school games I'm accustomed to.

For an old-school gamer,  I think the key is playing  5e for what it
is and not worrying about how you  might do it in your own games. It
is still  fun and  I'm enjoying  playing over a  gaming table  for a
change (complete with battle mat  and miniatures). But I don't think
I would enjoy running  such a game. I would try to  make it too much
like OD&D or whatever  and in the end, I'd think  to myself "Why not
just run OD&D?".

[1]: https://smolderingwizard.com/2013/11/15/carnage-con-report/
[2]: gopher://gopher.smolderingwizard.com/0/rpg/player_and_gm_resources/old_school_gaming_primer.txt