I found this out the hard way when I had a simple query that suddenly got very, very slow on a table where the application would constantly do a `SELECT ... FOR UPDATE SKIP LOCKED` and then immediately delete the rows after a tiny bit of processing.
It turned out that with a nearly empty table of about 10-20k dead tuples, the planner switched to using a different index scan, and would overfetch tons of pages just to discard them, as they only contained dead tuples. What I didn't realize is that the planner statistics doesn't care about dead tuples, and ANALYZE doesn't take them into account. So the planner started to think the table was much bigger than it actually was.
It's really important for these uses cases to tweak the autovacuum settings (which can be set on a per-table basis) to be much more aggressive, so that under high load, the vacuum runs pretty much continuously.
Another option is to avoid deleting rows, but instead use a column to mark rows as complete, which together with a partial index can avoid dead tuples. There are both pros and cons; it requires doing the cleanup (and VACUUM) as a separate job.