Disadvantages of JIT
A lean system has no resilience
. Integrating JIT as far as possible back up the supply line creates rigid connections between manufacturing units, leaving the entire system vulnerable to exogenous factors beyond management control: traffic jams, disruptions due to weather (hurricanes, for instance), accidents or catastrophes in one or another crucial segment. (And with JIT they're ALL crucial).
All production begins with nature - ores, energy, raw materials - and this sourcing, the root of the production process, can't be fully controlled.
A better model for management of production is the resilient systems of nature. Ecosystems absorb shocks and remain productive
(until they are dismantled by humans wishing to subject nature to human concepts of industrial efficiency.) The web of nature is resilient. JIT production processes are not. See Jane Benyus, "Biomimicry," for more on this.