To send 4k emails a month a 1€/month VPS running Exim is enough and takes 1h to set up. 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.
Deliverability is a thing. When most of your list recipients are on gmail, this is a good way to end up in spam for all of them. 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.