We have rough roads around here, lots of cracks, potholes, and 2" curbs. The tires I have here are only rated at 90 psi, not only would I be pushing the limits of the casing but also the rims at even that pressure. I've seen steel rims fold over and let tires blow out just from pressure.
On smooth road they will be fine, but I'm more looking to set this up for bike trail riding. The trails are mostly loose packed mulch here. Lots of trails through the game preserves and parks through wooded areas. Not rough enough to need a mtb, but too loose and soft for skinny tires. A lot of guys run the Kenda 1 3/8" knobby tires but then they suffer on the street with a soft tire and bumpy tread.
I want as much width as I can get. I wish I could find the Michelin tires that were on it but I'm sure they're long gone from production these days.
These tires are marked 38-630 but in actual measurement are only 29mm, no where near even 1 1/4" let alone 1 3/8". The old tires were almost 1 1/2" wide. I see this on a lot of bike tires these days, try finding true to size 26" x 1 3/8" tires for an old Raleigh sports these days, the tires are so narrow you risk damaging a rim.
Also keep in mind that these rims are wider than most, almost as wide as some mtb rims.