The issue with randomly selected representation is that the support staff start to become the ones who effectively make the decisions. This is the same issue with term limits (which to be clear, I'm in favor of, but we have to go in with our eyes open), which is that e.g. the congressional staffers gain power, especially if they persist across the end of the term limit. In these kinds of cases, you almost need term l…
Term limits are a bad hack trying to fix the problem that the status quo electoral system presents (1) too few meaningful choices, and (2) largely as a consequence of #1 and relatively stable local ideological mixes, features very strong incumbency preferences.
Fix the electoral system to resolve that (lots of ways to do that), and the broken idea of term limits stops being an attractive way to pretend that you are doing something without actually fixing the problems.