The SprintLink Peerless network is actually an IP-over-IP network, instead of a MPLS L3VPN network. Sprint engineers believed the IP routing technology to be mature and inexpensive, and viewed it as a better option than adopting new MPLS technology.
I mention this mainly to identify that there are different schools of thought on the available technology ...
Two main reasons for using labels:
It makes the transport layer independent of the customer addressing scheme. Multiple customers can have overlapping addressing. The transport doesn't care
Protocol independence. What you've describe works fine for IP, but MPLS can handle non-IP protocols (L2, pseudowires) too.