Is it common to seek outside letters for the third-year renewal of an assistant professor?
I don't know whether it is common, but a version of it, a 4th-year review, exists (determined by department pattern of administration) at Ohio State, and it's actually useful. It gives the candidate a good feel for what the actual tenure review will be like the next year, and alerts them to problems that can be remedied. Letter writers are usually asked to update their letter for the real review (though not if they wrote a crappy letter for the 4th year review). Similar letter-inflation exists in Alaska, Vanderbilt.

I take the point that this is a form of bureaucracy- and service-inflation, but it actually gives reviewers a longer time to read the papers, in case they are not familiar with the candidate's work. The problem-detecting function is quite valuable, I would say.