Yes dedicated email hosting will be cheaper. With shared hosting it's easy to see who knows their stuff. If they have limits in place on what resource you can use then as those limits apply to other customers as well as you then other customers cannot swamp the server. In terms of security they are getting good these days, my hoster will just shut down an account as soon as it's an issue, they actively scan accounts seeking out the problem ones and locking them until the owner sorts it out. Wordpress not by default will auto update everything limiting the fucktards that can't be arsed to update their wordpress and buggy plugins.
It's a fundamental risk of allowing arbitrary customer code from random customers to run on the same servers as you're hosting mail for other customers. You can try to limit resources, you can react, you can try to be proactive and scan for exploits, but you really can't solve this problem without completely sandboxing the users, and that means VMs or containers per user. Most shared web hosts don't do that, and when they do it tends to look more like Heroku or Google App Engine, not cPanel.
Why do you advocate for random unsanitized web code running on the same server hosting your mail, when you don't actually care about web hosting?
Why do you say these services do not tend to have redundancy or backups? you insist on not reading don't you. My provider provides 31 backups at all times taken once per day. Recently this allowed a customer of mine to recover their site that stopped working because two different plugins upset each other. I also doubt that there is one physical server, they work in clusters, never have I suffered an outage. on a virtual machine you are even more at risk as on there are no backups, that's your problem, it's your machine, it's up to YOU to pay for multiple virtual machines to cluster for redundancy.
The vast majority of shared web hosts throw cPanel on a bunch of servers and call it good. Each operates more or less independently. If that server fails, your mail is down until they fix it. They don't build a highly available mail architecture with multiple mail servers and distributed storage, your mail is hosted on the same single server as your web site. That single server *may* be hosted on a HA VM, but that still doesn't save you if it crashes, runs out of resources, has a major configuration error, etc. Nor does it guarantee availability during maintenance activities.
Not all shared web hosting works this way, but it is the vast majority, especially on the cheap end.
With regard to backups, on-host backups are common and generally pretty easy to access. It is usually completely opaque whether off-host or off-site backups are being performed, and at what frequency. Depends on the provider, but is difficult to verify and usually insufficient on cheap plans.
I'm not advocating for VMs, I'm advocating for buying the service you want- mail hosting - from a company dedicated to doing that, and only that, well. As opposed to one where mail is an afterthought/addon and that tries to meet the needs of hundreds of different web hosting customers at once, and all the random stuff they need on the server, and lets arbitrary customer code run on the same box hosting your mail.
I don't know why you write them all off, I have had shit providers and good providers, they are not all the same.
Unfortunately while I'm sure there are good shared hosting providers out there, there are lots that look practically identical, and the vast majority of them aren't great. From the outside it's hard to tell them apart, and since you are talking about $10/year hosting, most of it is on the crap side. Your host's cheapest plan seems to be $70/yr and seems to offer only 10GB of storage at that price. That is considerably more expensive than FastMail, and astronomically more expensive than Zoho or Rackspace.
If you care about reliable mail, just buy reliable mail. It's easy, costs the same, and you just don't have to think about it. Also easier for a layperson to manage.