Here’s an interesting thought: saving Bear Stearns increased risk in the financial system.
From Bank of America:
…the support of Bear Stearns appears to have unintentionally exacerbated the systemic risk of the Lehman Brothers’ default as short-term investors did not reduce their exposures leading up to the default despite the steady erosion in Lehman’s stock price and CDS spreads.
That leaves the potential interpretation that by supporting Bear Stearns, systemic risk from its default was postponed, but in having done so, unintentionally that action exacerbated the systemic risk resulting from the Lehman Brothers’ default.
After Bear Stearns, counterparties to banks were lulled into a false sense of security — assuming that default risks were reduced - or at least recovery rates increased - by a sort of faintly implicit guarantee from the US government against too-big-to-fail banks.
The principle example that would support that being the collapse of Reserve Primary — the money market giant which broke the buck the week LEH went under. Reserve Primary failed because it had bought a lot of commercial paper issued by Lehman. Commercial paper is, of course, unsecured.
Anyway, here’s what happened to the commercial paper issuance of both Bear and LEH in the runup to bankruptcy:

And the after-effects of Lehman’s collapse:
…money fund investors responded to the “breaking of the buck” issue at the Reserve Fund by withdrawing funds from “Prime” funds and placing most of those proceeds in Treasury or Government-only money market funds. That’s the 21st century equivalent of a “bank run,” and its consequences contributed to the severe freezing up of interbank lending in September and October.

_____