Revisiting TBTF

Mark Thoma pointed to Brad Delong's post on the Bear Stearns "bailout" which currently summarizes my view (emphasis mine):
We now have two precedents. If the Federal Reserve judges that a major financial institution:

1) is too big to fail in that its failure will generate systemic risk
2) has followed portfolio strategies that have produced inappropriate and excessive leverage
3) requires immediate action

then the Federal Reserve will intervene to structure and support a deal that leaves principals and investors in the offending systemic risk-creating institution with effectively zero entity. Counterparties will be rescued. Principals and investors will not--even if normal more lengthy legal and bargaining processes would give principals and investors a share of the equity value on the table.

This is not the arms-length equal-treatment impersonal-rule-of-law ideal to which a government should aspire. This does, however, seem to get the incentives about right. ...

These two precedents suggest that the Federal Reserve is evolving a case-law-of-twenty-first-financial-crisis that is somewhat different: in a crisis the lender-of-last-resort will always show up, but investors and principals in individual institutions that need to be specially rescued will discover that the lender of last resort is not their friend.

Contrast DeLong's view with Victor Reinhart:
The Federal Reserve's rescue of Bear Stearns Cos. will come to be seen as its "worst policy mistake in a generation," a former top Fed staffer said. ... The episode will be seen as comparable to "the great contraction" of the 1930s and "the great inflation" of the 1970s, Vincent Reinhart said Monday at a panel organized by the American Enterprise Institute, a conservative-leaning think tank where he is now a scholar. Until mid-2007, Mr. Reinhart was director of monetary affairs at the Fed and secretary of its policy-making panel ...

When I saw the following linked post - If half of the people who start a course pass it why can't I conclude that 100 people started the course if I know that 50 passed? - I thought it might have some application to TBTF but I was wrong. It just led me astray for awhile but it was interesting nevertheless. I've come round to the point of view that TBTF rescues are analogous to the 'peso problem'. In the peso problem a stock/currency trades at a premium because there is a small risk of a very large loss. In TBTF, regulators fear that there is a small risk of a large and systemic disruption in the market. This is where the analogy ends.

This would lead regulators perhaps to intervene "more often than they should". Regulators observe x number of failures. Of this, a small proportion, p would lead to a systemic crisis. Unfortunately, we do not know what the true value of p is.
1. Can we estimate p?
2. Is it useful to estimate p?

If regulators were risk-averse, even if we had an unbiased estimate of p, would regulators intervene more often than they should?