John Thain, who was himself saved by Bank of America that weekend, thinks that letting Lehmans fail was a huge mistake:

“Allowing Lehman to go bankrupt was a tremendous mistake – it led to hundreds of millions, if not trillions of dollars, in losses.”

Niall Ferguson,  who has edited a book on counterfactual history, thinks not, in a thoughtful (and mocking) piece in the FT, "Why a Lehman deal would not have saved us"*

 The critical point is that, like Bear Stearns, Lehman was just an extreme case of a general phenomenon. A relatively small number of very large financial institutions had become dangerously leveraged and were on a fast track to insolvency as their property investments imploded . . . What was needed was not a succession of ad hoc government-backed takeovers. As Ken Lewis, Bank of America’s chief executive, came to realise when he looked more closely at Merrill Lynch, today’s buyer risked being for sale tomorrow, since no one’s balance sheet was safe . . . if Mr Paulson and Mr Bernanke had taken over Lehman on their own initiative, there would have been an outcry in Congress against yet another handout to a manifestly mismanaged institution. There might very well have been no Tarp. That surely would have been a death sentence for Citigroup, an institution three times larger than Lehman.

Good point: if not Lehman, then then next bank instead - eventually, the political will would have run out, and with it the bailout money.  Then it might have been FAR worse.  

This is the sort of thoughtful analysis the BBC could have done with in their terrible programme about Lehmans.  Unfortunately, television producers generally assume that programmes about finance must not be too ambitious and attempt anything like, say, explaining finance.  That might worry their viewers, who can instead be left with the comforting notion that Lehman's fell because it was run by wicked greedy people.  Ban wickedness and greed, then we'll be fine.

UPDATE: John Cochrane takes an even more hardline view against rescues here.

"This crisis pushed our government close to its fiscal limits. The next one will be beyond what even our government can contain. " 

*yes I know I don't have a great record in praising Professor F, so credit where it's due.