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.
There are other factors like IP reputation of the email server sending the email. And if you’re using a hosted service, there’s no way to control those IP addresses.
I run my own obscure mail server and have not had an issue in years, except for ATT[1]. I'm super low volume - I run mail for about 20 humans, a few mailing lists, and some other automation that does things with email.
I do things correctly - I mean, I run nearly the same stack/configuration (scaled way down) as I do professionally for my employer, which delivers 8 digits of messages a day all over.
But that doesn't explain why I don't have problems and others do - lots of people get this right and still have problems. And I think that comes down to the fact that mine has been on the net since the mid-90s. So, unfortunately, I suspect the answer to a lot of these problems is 'exist for long time' - until your MX is associated with a bias towards "not spam" in everyone's filters.
I can think of ways for existing mail servers to vouch for new ones, but I don't think there's any reason for established ones to want to do that, so it wouldn't work. I'm not sure what the answer is.
[1] And after many, many years of attempting to resolve it, they can bite me. I got annoyed enough that they get a custom bounce from me now on the rare occasions someone tries to spam me through them.