As a business, I wouldn't do it until the cost of the bandwidth+hosting exceeded the cost of an extra, dedicated employee to manage the VPS server(s).
Why do you think you don't need that extra person to manage the instances in a cloud setup?
My experience is the reverse: It tends to take more man-hours per instance to manage a large cloud setup, because there are many more spinning wheels. The overall complexity is often vastly larger. In fact, I have clients I manage physical servers for where the time taken per server is on average still far lower than for cloud instances even including the 2+ hours lost on travel per visit to one of the data centres if someone has to physically go in (rather than rely on "remote hands").
This is before factoring in typically higher utilization rates for the dedicated hardware, because it's easier to customize it to get the right balance of RAM, CPU and IO for your workload. The result is usually fewer dedicated servers than you would have cloud instances.
Working is better than not working perfectly.
The hosting company takes care of the VPS servers, just like Amazon takes care of the AWS servers.
I'm not saying don't optimize, but I am saying that you shouldn't switch infrastructures unless you are saving enough to cover additional talent.
Just buy dedicated servers or VPSes, no datacenters or staff needed. The hosting provider takes care of the servers, staff and the datacenter.