Thinking about it, the problems with accelerating the growth of the Not-Banks are even worse with the Chicago Plan than with OTL.
The key issue is that companies need finance. They can get it directly, through issuing bonds, or they can get it indirectly, by borrowing money from intermediaries who take deposits or issue bonds (or both).
Issuing bonds is expensive, so only big companies do it - small companies, in OTL, borrow small to medium sums from deposit taking banks.
Now, under the Chicago Plan, all the corporate finance gets funnelled thru Lending Companies, who can't take deposits.
Therefore all "small finance" - critically *including* mortgages to householders, has to go thru Lending Companies ... who cannot access the funds at Deposit Banks but need to go to the bond market.
Therefore, when these entities start to fail, they keep failing, and commercial credit freezes.
Just like OTL 2007, really, where the FDIC-insured Banks were overwhelmingly ok, and anyone reliant on commercial paper was in a lot of trouble.