I do agree however IP reputation matters. If you share an IP with other hosters, or your IP has been recycled from a bad reputation IP, or you have a residential IP or have found your way onto any of the email spam lists recently, or been reported for abuse or marked as spam enough times by freemail service users, you may have trouble getting to 'inbox' and eventually even getting delivered. Reporting systems like DMARC should let you know, however, before it becomes serious.
I don't think running your own email is a high maintenance activity that some suggest (especially for small servers) but it is definitely more effort than outsourcing it to someone else. I'm glad services like this exist, if only to prevent email becoming a Microsoft-Google walled garden.