I myself like to do this. But only for home servers. I would never do that for a "serious" application. There are several reasons, the most important one being that this is a perfect example where outsourcing the work is both cheaper (economies of scale), more reliable (parts are tested better) and less risky (companies which do that at a larger scale have better risk management). If one the SSDs dies he has to drive there and switch it out, instead of one person simply doing that for the whole data center. This is simply inefficient.
And of course Amazon hosting is more expensive. It is more flexible; you can spin up instances at your whim. You pay for that. It would be better to compare it with standard dedicated server hosting.
Have you worked with "professional support" in a colo before?
When a hard drive dies under vendor support, one guy from the vendor drives out there to replace it. Half the time they don't test it after it's replaced unless you request it. Sometimes the parts are duds. Sometimes they bring the wrong part, or it doesn't fix whatever was broken on the server.
If it's the datacenter's remote hands, it can be hours, and on rare occasions days, before somebody starts working on your issue or even answers the phone or e-mail. Same issues come, and you have to have your own spare hardware for the remote hands to use.
It's highly variant based on the datacenter and vendor(s) and other issues. There's no guarantee that outsourcing will be reliable. You have to find the best one possible and build a good relationship.
Having done this twice before, I strongly, STRONGLY recommend picking a colocation center that's less than an hour drive from someone who works for the company. Or you.
Just in case, but that does come up from time to time and if it's many hours away (or worst of all an airplane ride) you will get hours/days to fix things as you noted.
The shop I worked with, we had support on the machines, so Dell would send a tech out to replace a part for the servers that had valid support contracts. We still needed someone on the phone to remote-in to test the fix, of course.
For more complicated problems, our main colo was about 45 mins away from almost all the SAs. We used remote hands for colos that were an airplane ride away, and had varying (read: sometimes really shitty) results.
And of course Amazon hosting is more expensive. It is more flexible; you can spin up instances at your whim. You pay for that. It would be better to compare it with standard dedicated server hosting.