If they truly have to handle a massive amount of traffic with only four people, a service like Amazon is a pretty good deal. It makes it trivial to create, clone, archive, or upgrade servers, and you never have to worry about drive/CPU/motherboard/RAM failures bringing down your site at 3 AM.

As someone who's worked in a data centre before, I can say hardware problems only increase as you scale up. We had around 350 servers with an average of three drives each, and we probably went to the data centre to swap dead hard drives on average three times a week - SAS, SATA, or SCSI. Nevermind the time I spent testing motherboards, swapping CPUs out, etc.

Owning your own servers means dealing with maintenance and downtime. Virtualizing 10 servers on one physical server is great until that one physical server's RAM starts acting flaky, and then you have to take those 10 servers offline, or shift the VMs onto your other hardware.

Renting your servers typically means paying a monthly cost for the hardware, including RAM and disk, long after the fees have paid the DC back their costs.

For Reddit, being able to bring N extra nodes for X purpose (mysql, cassandra, web serving, etc.) with a few clicks in a few minutes is likely a huge draw for them. It means they can grow gradually (instead of having to shell out another $10-20k for a new server), and it means they can dynamically adjust to meet their needs. For example, if Monday is a busier day than Saturday by a significant stretch (and if their architecture allows it), they can bring more nodes online early Monday morning to handle the load. Take them offline until Thursday evening to handle the 'It's Friday, to hell with doing work' rush I'm sure they get, and so on.