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 stacks.
In theory, MPLS should have brought us less-expensive backbone (P) nodes which didn't need a full IP routing table. This would've made networks look a little more like the IP-over-ATM and IP-over-Frame-Relay networks of the mid-90s and late-90s. However, in practice, vendors did not ship economical MPLS P boxes. Indeed, Cisco and Juniper both shipped numerous products that could be a PE but not a P; examples are many Cat 6500/7600 cards, and early EX-series switches.
Touching on some history, again in theory, an ATM or Frame-Relay switch or entire network could have functioned as an MPLS P node, being configured by a separate control-plane. To my knowledge, no such networks were ever deployed in production. However, the desire to offer this capability resulted in a number of MPLS protocols' design decisions, for example, per-interface label allocation.