Keep in mind that many of the discussions about tire vs rim width seen today are referring to bikes (used primarily off-road) where a tubeless tire is likely going to be run at the limit of low pressure, for both traction and bump absorption. These discussions don't really apply to our vintage road bikes at all!
A narrower rim will reduce the mounted tire's width by almost half of any rim-width reduction, and also slightly reduces the mounted tire's height.
In the 90's, I raced XC on 700c Mavic MA40 rims measuring 13mm inside, with 700x45 Panaracer "Smoke" tires fitted. I had no issues at all with this setup, other than some difficulty fitting tires and some difficulty getting said tires past the pads of the centerpull brake calipers.
Shown below ripping a corner at speed on those very wheels, following which I almost struck a photographer who had strayed too far into the outside line of the corner!
Narrow, double-walled Araya rims from roughly the 1980's weren't actually hooked, but had semi-hooked sides featuring but a semi-circular nub instead of a sharper-edged feature found on their contemporaries from Mavic, Wolber and etc.
As such, these rims can release a tire while riding, particularly when the tire is somewhat aged with the rubber surrounding the bead having lost it's flexibility and it's grip.
I have had two such blow-outs using these rims with aged tires, one of which had a wire bead and the other having a folding bead.
In both cases, the blow out followed sustained, hard braking following a descent, with a few thumps against a fork leg before the actual explosion. Neither tire suffered damage and a fresh inner tube got me home, and I never fell off (due to the warning thumps).
In another case with these rims, a thrift-store Bridgestone 500 model blew off an aged tire after having been re-inflated, again with no tire damage.
High spoke tension is another factor in whether such a rim might release a tire's bead, and my own spoke tensioning goes beyond what typical production bikes came with, reducing the rim's diameter slightly.
Continental tires tend to give a more reliable bead retention on the few bikes I've had where a rim tended to let go of tire beads due to poor diameter tolerances and other factors.
Thicker rim tape, laid wall-to-wall inside of the rim, is known to prevent any section of a tire's bead from rising up near to the rim's edge.
