The real advantage is to have control over your own infrastructure and ensure the privacy of your reader base.
The drawback is having to monitor blocklists and the reputation of your server IP address.
Which sound like big drawbacks for anything reasonably serious. Maybe if you're doing this at scale for clients but, then, you're potentially exposed to clients who can cause problems that affect other clients.
People who believe this is a viable method to reach the inboxes of thousands of gmail users have never tried.
Real Soon Now(TM), the tech community needs to start a serious campaign to shame and isolate email providers that do not reliably deliver legitimate emails, regardless of how high profile they are. It probably needs meaningful government/regulator backing to get anywhere. The odd false positive on spam/malware filtering is understandable, it's not a perfect science, but the reality today is that a lot of these services simply don't work properly and the unreliability is probably causing some degree of damage to huge numbers of people and businesses. Email is far too important for far too many things to let the reliability continue to degrade according to the arbitrary whims of a few large mail services and to permit oligopoly effects to lock new or small-time providers out of the system almost entirely.
I have had customers contact my business to ask for help with something, and we send them a quick reply answering their question, and then the next day we get a frustrated follow-up asking why we are ignoring them, and this continues for another round or two until they give up on buying something from us or cancel a subscription.
I have had friends send me a reply a month after a big party saying they're sorry they didn't make it but they only just found the invitation and the follow-up I sent them in their junk folder.
Those sorts of cases are annoying and seem to happen all the time these days, but imagine if a missing email was something really important from your doctor or your kid's school.
You're free to try to educate users now, if you like, but most people receive emails only from a small group of hosting companies.
The actual people being negatively affected have chosen an acceptable level of spam false positives.
Unless the user is actively expecting to receive an important mail around a certain time and therefore likely to notice its absence, the failures are either quiet (messages dropped in junk automatically that may or may not be noticed by the recipient later) or totally silent (as with ISPs that drop mail they deem inappropriate entirely, without notifying either party).
Even if someone is expecting a mail, as the experience with business customers I mentioned demonstrates annoyingly often, the failure to receive that email may be assumed to be the fault of the expected sender, not the recipient's own mail service.
You can use a VPS for web projects. For e-mail you'd want a dedicated server with a separate IP that is going to cost you €40/month. Yes it may take 1h to set up, but gaining reputation takes time - you definitely won't be able to reach all recipients within one hour of purchasing the server.
I sent emails from a VPS for years without issues. I stopped purely because Fastmail had better software and cheaper storage.
From experience I can confirm the reputation build-up requirement though. And all that reputation can get ruined by a single blacklisting - even if you manage to get the server de-listed later the damage is done.