Leased lines (also known as private wires) have been around since the days of the telegraph.
The same transmission technology is used in the local loop (and sometimes in the backhaul from the local exchange to the switch) for packet/frame/cell switched technologies (X.25, Frame Relay, SMDS, ATM) as in contemporary leased lines. Note : MPLS is not a transmission technology; a leased line could be changed to an MPLS link just by changing the software in the routers at each end. *1
With a long-distance leased line, resources are dedicated to the line in the telco backbone network (amplifiers and pairs in the early analogue days, timeslots in the PDH and SONET/SDH days). This requires more circuits and equipment than an MPLS network, where oversubscription of the bandwidth is usual. It was usual that the PDH data network was separate from the voice network, leading to further costs.
Therefore, telcos have been able to price MPLS and its predecessors more competitively than leased lines and have gradually phased out the latter. In the UK, Megastream services were still available for sale up to December 2021, but I doubt many circuits were sold for data in the 21st century (non-data leased lines still have their place in railway signalling and air traffic control, for instance).
Apart from the cost savings available, a company wishing to connect a number of sites together with leased lines either has to create a central hub with the capacity for one link per site (and take a risk that a failure of the central site shuts down the entire network) or lease extra lines to create a mesh.
With a packet/frame/cell/label switched network, the mesh is created by the router configuration and alternative routing is easily set up.This was an important reason in my personal experience managing a network of about 30 sites for replacing the multiple hub and spoke leased line network of 1993 with Frame Relay in 1998 and MPLS in 2003.
Another possibility offered by MPLS is the ability to mix public Internet access and private networks in the same local circuit and CE router. The CE router is not limited to one private network, so a multi-tenanted office could provide MPLS access for different tenants to their related sites with shared equipment. This requires a level of trust and bandwidth mix which seems unlikely to me.
*1 The introduction of fibre services changed the bandwidth available but not the nature of the services; long-haul Gigabit Ethernet was available on a leased-line basis in the early 2000s.