As far as I know, there is no reasonable logic design
using transmission gates that can't be restructured to use something
else instead.
Probably true but some designs using transmission gates are so incredibly elegant. Look up
Caldwell
and Keister-Ritchie-Washburn and you will find that there are some classes of problems
that are handled very nicely with transmission gates (AKA relays) but are cumbersome with
more modern symbology. This class of problem is broadly called "iterative
networks". And these are real world problems important to designers of low to high
complexity systems in that era. Interestingly, since the modern tools no longer make these
problems feasible, hardly anyone tries to solve them with the same efficiency anymore.
(Some of the combinatoric problems that are easy with iterative networks happen to overlap
closely with classic cryptography BTW.)
Transmission gates are really a hardware optimization,
and not part of pure digital design.
Maybe, if you definition of pure digital design limits you to NANDS for example. But all
the logic design handbooks/textbooks up until the 60's were inclusive of transmission
gates as basic elements.
Tim.