It is increasingly difficult to not use one of these "free" email services because of their aggressive blocking of any autonomously operated email servers.
Has Fastmail ever been blocked?
I've used a paid email provider since before Gmail existed. They've not been blocked.
I know there are the occasional posts on HN about Gmail blocking their servers, but I doubt it's anywhere close to the norm.
No, but I do think that everyone who gets a service for free should by default assume they don't have much privacy. That is not a huge burden to assume.