The way Fastmail is setup is that there's a master administrator login for each account, and then you create email addresses under that account with their own logins.
So if you somehow lose control of an email login, you can just get your administrator to login and reset it for you.
Presumably if you needed the administrator account reset, you would have to contact Fastmail support, but you don't tend to log in to those much at all so there's less chance of them being stolen.
I use mailgun to send automated alerts from our home network backup processes and security cameras.
When sending to a Gmail account, there is sometimes up to a 2 hour delay before the mail arrives, though usually it's within a few minutes.
Mail sent to a Fastmail account always arrives almost immediately.
MG does some kind of prioritizing based on the domain when using their free account. It's obviously an anti-spam measure. They might also have some kind of "warm-up" feature where if you send enough email with a valid FROM and TO address then they queue it faster, IDK. Not sure if they do the same thing with their paid plans.
My understanding is that they rate limit the number of emails sent to a domain per IP address, per hour. Email service providers assume that if you send "too many" emails to their domain per hour, it's "spam".
The same thing happens with my dedicated IPs (sending ~500k/mo). Yahoo is frequently rate limited. Gmail is less common, though we have years of good reputation on those IPs.
Our product is a SaaS for pet service businesses (grooming, dog daycare/boarding, training). The app has 34 distinct automated email types that are sent at various points. It's a lot of email :).
Since FastMail is a paid service, FastMail has actual customer service. Additionally, they have information about your payment methods on file, so they have more information that can be used to verify your identity than the average free service. I do not know their specific policy on what level of identity confirmation is required though, if they do indeed allow account recovery in this manner.
You can, of course, get an account recovery code, or reset using your phone, as is pretty common.
A key difference though, regarding support, is that if your account gets suspended, there's a path with real humans to get it reactivated. Most Google account issues I've heard of aren't "loss of password" so much as "Google has banned you and has no appeal process".
Regarding deliverability of incoming mail, I will say I've found their web client refreshes faster when inbound mail comes in than Gmail, and when waiting for mail from other common services I've found they arrive faster since switching from Gmail.
It really is crazy fast. I get notifications from my browser and phone about new emails almost simultaneously. And if I read the notification on my browser, it instantly disappears from my phone, and vice versa. Honestly, it works how it just ought to. Can't give higher praise than that.
I've been super happy with Fastmail. Can't recommend it enough. The stuff they're doing with JMAP is really nice too -- should give it a read if you haven't seen it before.
FastMail even supports push notifications for Mail.app on iOS (which AFAIK has previously been limited to iCloud accounts, I think possibly Exchange, and, oddly enough, Yahoo).
Also if something goes wrong is there a mitigation plan in place to recover data and restore access of the user?
That's another major concern - to lose access to the account and not be able to recover it - because Gmail has no support.