Tires have a function you might not have considered: cushioning the rims from road shocks. If you have tires which are too narrow they are also not tall enough, and they might allow the rims to have hard impacts with the road surface especially if it is not perfect. You need enough height AND pressure to inlulate the rim from road bump damage (one aspect of the safe side), not so muchpressure that other new problems are initiated in the tire/bead/rim, and not so much pressure that old flaws and damage sites in parts are over stressed and a hard failure is accelerated. The first "safe side " is about tires not too soft. The other two "safe sides" are about tires not too hard. You need to understand and adhere to both conditions to get comfortable, lengthy service from your wheels including your tires.
The wheelbuilder I was talking about is Peter White, who publishes his opinions and policies on his website, from which he also sells retail and wholesale. I'm not saying to go get new wheels built, but there are a lot of experts out there, and this is one I would recommend reading.
Another one is Jobst Brandt, and another one is Sheldon Brown, both now deceased. Most likely not everything they say agrees three ways, but it's worth a look.
It's absolutely a fact that wider rims are stronger than narrower ones. If you are road racing, you probably should get a set of wheels built with tubulars, but get someone like Peter to design them for your size and weight and intended usage. If you are also going to commute with your common load of gear you carry, have a second set of wheels which work with a more durable wheel. Seriously, reallty good wheels these days have nearly zero problems with bead separations and blowouts. They really can be nearly trouble free these days.
Tubulars eliminate some of the tire bead problems that clinchers can have, but the need to be glued well to the rim. But the really can handle big pressures at 21 mm widths.