I'm in the middle of relistening to MTT, and I was struck by Housman's thought as he was bicycling from one end of his Delfac works to the other that it would unfortunately be some time before there would be pneumatic tires.
Thing is, there's no obvious way they'd break the proscriptions. It was previously established during the assassination attempt against the Empress in Corisande that Safehold has a rubber industry. Indeed, it's the sort of simple transportation improvement that the archangels encouraged that I could easily see tubed pneumatic tires being given by them in the Writ. Assuming it hadn't, the only reason I can see why pneumatic tires wouldn't already be available by the time would be that it was a low priority item not worth a direct push from the Inner Circle and thus would need to wait for a Safeholdian Dunlop to have the idea on his own.
As an aside, to discourage the development of tires suitable for high speed applications, describing bias-ply rather than radial construction in the Writ would be a good idea from Langhorne's POV
