I can understand being nervous about some cron job running on some other service, but what's concerning about a cron job managed inside of Postgres with pg_cron? If that doesn't run, your database is probably down anyway.
Postgres might cost more but I'm probably already paying. I agree that exhausting connections and writing at a high rate are easy ways to bring down Postgres, but I'm personally not going to worry about exhausting connections to Postgres until I have at least a thousand of them. Everything has to be considered within the actual problem you are solving, there are definitely situations to start out with a cache.
I might be ok with this if it were built in, but pg_cron is an extension, so first off you might not even have access to it. And then you still have to monitor it.
Seems like it's available on all the major providers.
Heroku doesn't have it. That's actually kinda annoying that they don't, cause the others do. AND they no longer have free Redis, so that changes things a bit.
Edit: well a tiny bit, max $3/mo