'Stay on host email, it's simplest' — the deliverability tax

Heard this week: an agency's transactional emails kept landing in spam on a managed plan. Word is most managed WP hosts run transactional mail through a shared relay with a battered sender reputation, or disable PHP mail entirely and don't tell you loudly. A source in deliverability says the 'included email' is the first thing that silently degrades after a host gets acquired and consolidates IP pools. The advice to 'just use the host's mail' inherits someone else's spam history.
Watch this: when a host starts pushing a third-party SMTP add-on, their own relay is already on a blocklist.