This is a misunderstanding of lean manufacturing. Lean is not about eliminating every stockpile, it's about thinking through your supply needs and only stockpiling what is necessary.
And then multiply across everyone in a supply chain for a single product having to deal with waiting to receive giant parts orders from their vendors before they could start their own giant order to supply their customers.
Think of each stage of the system, not just the components you bring in but also the partially assembled components you produce along the way as well as the finished product. US auto manufactures (in particular) had an operating method where they kept inventories high at all stages. This wasn't entirely deliberate. They weren't saying, "We need 5000 car doors just sitting here." They were, instead, saying, "We can't stop making doors just because everything else down the line is stopped due to <event> so keep churning them out and pile them up." The tail end inventory of "complete" vehicles were sitting there due, often, to quality issues (misaligned assemblies, missing parts, whatever the reason may be).
So inventory piles up everywhere along the chain, which also worked because there was a large turnaround period when retooling and equipment downtime (not always planned). Because Nobody Ever Gets Credit for Problems that Never Happened [0] there was an underinvestment in maintenance and improvement efforts. High inventory across the line papers over this issue. Lean discourages high inventory in order to make these issues apparent so that they can get the attention that they deserve. Also, rework is viewed as waste so quality issues should be addressed when they're discovered, not by assembling hundreds or thousands of vehicles incorrectly and then fixing them, fix the assembly line issues causing that misassembly.
[0] https://web.mit.edu/nelsonr/www/Repenning=Sterman_CMR_su01_....