I pulled some very hard 21 inch tires off a couple or rims. I did not see the flap in the one tire till I went out to take some photos. The (brown) white Riverside tube was in the Riverside tire the other one is an off brand but has a flap in it. The flap is not a cut down tube. I should add the tire with the flap was very worn.

I once had a tube, a red Goodyear for a 30 X 3 1/2" that held air for maybe 15 minutes b4 sitting on the ground. When I pulled the tire off the rim and removed the tube I counted 13 patches on it. One even over lapped another one. Pulled a 20" tire off from a rim I picked up two weeks ago at an auction that was flat but not one patch. My guess it may have held air when last taken off, no Nails that I could fined.

I tried putting air in both, no way it cam out as fast as it went in. I think the two tires with rims and wheels must have been stored inside an appliance store for at least 40 or more years when I got them. Just plain dry rot.

Mark, I pulled two red rubber tubes from two Goodyear Pathfinder tyres mounted on 30 x 3.5" BE rims. The tyres, tubes and rims all looked new, but the tyres were so hard they broke! The tubes were perfect and I have them both in service.

Your old tyres are straight sided tyres, and they are correctly fitted with flaps. Can you imagine trying to keep that unjoined flap and the valve stem in place while trying to mount a clincher tyre?
I took one off once. One end with the hole in was in place around the valve stem. The forked end had migrated around the tyre and was between the tube and the tread side of the tyre. I guess under inflation could have allowed this shift. I guess tyre balance was not something of concern. All that extra weight combined with the metal stem would have been considerable.

Allan from down under.