Storage is the most costly element of hosting now days, since bandwidth is practically zero cost. Shared computing power brings down the cost of ram/cpu resources.
But VPS space is going to be plenty for a typical website, its probably only an issue if either you have a huge database, or its a media heavy site.
There is one person I know who took 100s in donations every month, to cover hosting costs, on top of that he had adverts, the thing is, his hosting costs were about a fiver a month, I know because I was his host. So I tend to take it with a pinch of salt when people go on about hosting costs, now of course if you pay for "managed" hosting, its a different kettle of fish, since there is a premium to be paid for that type of service.
For my own hosting I have the following.
4 dedicated servers, 3 of them which are been utilised as virtual machine hosts. Since thats a much more efficient to utilise hardware.
2 VPS, these dont really host anything, I use them for DNS services and VPN end points.
VPS are a very useful platform these days, not just for the cost but also for the fact you can usually upgrade resources without any significant downtime or having to move data around.
Cloudflare also can significantly decrease costs, as only uncached requests would make it to your server, plus they will absorb DDOS for you.
There is expensive providers out there, but its like on the domain renewal discussion, I feel they get customers paying them simply for them been "known" and not prepared to shop around. A lot of people also likely pay for "managed" services without realising unmanaged its not that difficult to do. Or even pay for a sysadmin that would typically cost a fraction of managed hosting fees.
Take Leaseweb as an example, you can get cheap hosting from them, but of course be prepared for no included remote hands, and long support times, but for most people neither of these are not particularly important. For dedicated hardware check places like soyoustart, hetzner auction servers, kimsufi.
Hosting from home I have never been a fan off, the way I have always seen it, is that since hosting costs are so cheap, it feels like you saving pennies with too many downsides, a datacentre gives you multi homed redundant bandwidth and power. Also assuming the server is rented not colo'd they will also deal with hardware failures as well.
Also that fansite you mentioned if they are paying for the domains it perhaps does make some sense since its very likely that costs them significantly more than the actual hosting.