|Monitoring the pieces is NOT the same as monitoring the whole.|
But there's one major gap in this approach: you're missing end-to-end monitoring.
I've been thinking about this situation lately. It's a result of a problem from earlier in the week. Some VMs were reporting very high disk latency (spiking between 100 and 200 ms). And as usual, the storage engineers said that the SAN was fine, the virt guys said that ESXi was fine, and the Windows guys said that the VM's OS was fine. So in the midst of every piece being "fine," we had a VM in trouble.