Should one avoid erudite vocabulary in statement of purpose?
Erudition and eloquence are useful tools for academics to possess.

However, excessively erudite writing can become opaque. That's not what you want to achieve in scholarly writing. Scholarly writing should be lucid, informative, and as direct as possible. Thus, using "five-dollar" vocabulary when "fifty-cent" words will do probably distracts from your writing overall. On the other hand, if that five-dollar word is exactly the word you need in a given situation, don't be afraid to use it. It's better, in my opinion, to moderately challenge the reader in a concisely written text than to be long-winded.