Should Private Equity Funds be allowed to buy into Banks?

Desperate times call for desperate measures. That seems to be the thinking behind discussions whether or not it should be made easier for Private Equity (PE) firms in the US to invest in regulated banking firms.
But given the fact that Private Equity essentially is a way to generate returns through leveraged investing in assets it appears illogical to allow Private Equity players to invest in banks at the current time.
The present credit crisis has demonstrated that the banking sector is more than others dependent on the confidence of investors and depositors. Excessive leverage is one key factor that contributed to the current malaise in credit markets. If it would be a pre-condition for allowing Investors access to bank shares to invest on an un-leveraged basis how would they make money? How much could PE Investors improve the management and profitability of banks without recourse to financial engineering? Do they really have superior management skills to offer?
The ultimate investors in the private equity funds could easily invest directly in the shares of banks directly on an un-levered basis - and save themselves the high fees at the same time.
And how committed are Private Equity firms to their investments? Their 'funds' are constructed in such a way that each investment is held in a separate legal entity (often domiciled in offshore tax havens) which allows them to walk away at any moment from any investment that does not 'perform' as expected.