It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. In the talk, I will answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space. This class contains all non-Archimedean Polish groups, for which there is an alternative, game-theoretic proof giving rise to a new criterion for non-essential countability. I will also discuss the following variant of a theorem of Solecki: every infinite-dimensional Banach space has a continuous action whose orbit equivalence relation is Borel but not essentially countable. This is joint work with A. Kechris, A. Panagiotopoulos, and J. Zielinski.