Earlier quoted context omitted.
Out of curiosity, if the problem of connections being expensive is solvable by PGBouncer-style connection multiplexing, why doesn't Postgres just do that by itself?
Because pgbouncer's transaction-based pooling, which is what the previous poster was referring to, breaks a few postgres features. This is fine for most applications, but not all. See the table on https://www.pgbouncer.org/features.html
Essentially, a "please serialize everything (temp tables, SET GUC values, etc) from this session to disk and load it back when necessary".