Do long transmission lines degrade rise/fall times, and if so, by what mechanism?
Yes, there is such a effect.  A ideal transmission line is modeled with lots of little series inductors and parallel capacitors.  See this answer by Phil.

In such a ideal transmission line, frequencies above a certain amount are removed and the remainder of the step propagates forever unchanged.  This approximation is usually good enough for "short" transmission lines.

Real "long" transmission lines differ in that the series resistance matters, which is ignored in the ideal model presented above.  This series resistance effectively adds some low pass filtering.  Since the resistance accumulates with length, the resulting filter becomes ever lower in frequency.  The more low pass filtered edge at the end of a long transmission line therefore looks more spread out since ever more high frequencies are removed over the length of the transmission line.