I think in practice there have been a few historical problems with this approach. A major one is that while in theory it's possible to secure a process to a chroot jail (either the Linux or the BSD variety) in practice it's hard to defend against arbitrary, possibly malicious programs in that jail.
Kernel exploits that rely on local access are uncommon but not incredibly rare. You could easily have a hosting service like this that ran fine for a few months, or even a few years, and then a 0-day kernel exploit comes out (that relies on having local access to the machine) and then you're SOL.
Another issue is that in practice some system calls are very expensive. With a little knowledge you can DOS a machine hosting your process if you can run arbitrary system calls -- for instance, if you can create some sort of resource that is expensive for the kernel to track, and then create a lot of that resource. Sort of related to this, at least in Linux there are a very large number of syscalls and new ones are added relatively frequently, and not all syscalls have had the same amount of security auditing.
Even if you're not worried about your own servers getting hacked, you need to convince your customers that other users aren't going to be able to intercept or modify their data or attack their VMs.
In my mind, one of the main innovation of a lot of the VM stuff in recent years, and in particular the NaCL approach of limiting what system calls can be invoked, is that you are fundamentally reducing the interface by which malicious programs have to attack the hosting machine. If you can securely limit system calls to a small subset, you can more easily audit the paths those system calls make to ensure that they're secure and can't be used in a DOS scenario. In a virtualization environment like Xen or KVM, the amount of code that you have to audit is limited to the Xen/KVM code which is much smaller than the rest of the code base.
Just my 2c., etc.