MPLS-TE - why are IGPs necessary
IGPs are vital for the operation of MPLS in general. An MPLS network involves an overlay network composed of MPLS label switched paths that are established between MPLS routers. This is where the MPLS mechanisms operate. It also includes an underlay network which is the physical infrastructure and the IPv4 or IPv6 network that supports it. This includes routers as well as the IP routing protocols running to make the underlay operational. Protocols such as OSPF, IS-IS, as well as EIGRP can be used for this purpose.
Strictly speaking, it is technically possible to create an MPLS topology without the use of an IGP (i.e. you can use purely BGP for the underlay network or you can use static routing between routers) but it is typically not recommended. IGPs are much faster in converging and deliver a higher degree of efficiency of operation.
Now, specifically for MPLS traffic engineering, IGPs are indeed vital. TE involves optimizing the performance of a network by dynamically analyzing, predicting, and regulating the behavior of data transmitted over that network. IGPs like OSPF and IS-IS with traffic engineering extensions (OSPF-TE and IS-IS-TE) can distribute not only the routing information but also the traffic engineering information like bandwidth, delay, etc. across the network. This information is used by MPLS to create Constraint-Based Routed Label Switched Paths (CR-LSPs), which are optimal paths from source to destination satisfying certain constraints like bandwidth, delay, etc.