Overall I agree with you - no one should be dumping stocks and funds now.  The time to sell, if ever, is when you look around and everyone is going crazy for stocks, to the extent where no one is talking "sell" and P/Es are out of control (i.e. 1999).  Selling stocks in a bear market makes no sense unless you face emergency needs, which is a failure of asset allocation.

My objection is to your reasoning, which is dubious.  AMFs have no proven record of preserving capital in bear markets, and in fact that is not their job - if they tried to do it they would only lag indexes by more in the bull markets.  If you need to preserve capital, then you should allocate more to less risky investments. 

I don't think I can beat professional managers or index returns, because due to the hard work of professional managers almost all stocks are very close to fair value.  Unfortunately, this is a problem for professional managers who have to beat their peers and the market by enough to make up for their expenses.  That's why I believe it's most rational to invest in index funds (low cost, diversification) or individual stocks that I plan to hold for the long term (even lower cost, chance of windfall profits).  If I buy an actively-managed fund it will be something with low costs, low turnover, and proven expertise like Primecap.

I'm still young, so I'm investing relatively small amounts of money that I could afford to lose.  There's no way around risk in the stock market - it's always there, and it could always wipe you out.  At the same time, based on the best information available to us, the stock market always has positive expected long-term returns in excess of those for other asset classes, so the only reason to hold out of the market is if you need money in the short-term.  In that case, you're better off increasing your allocation to Treasuries/short term bonds/MM/cash rather than relying on mutual fund managers to preserve your capital and yourself to not sell at a poor time.  Nobody saw some of the biggest crashes in history coming - Peter Lynch was on vacation during the 1987 crash.  That's ok, because no one should sell in anticipation of or response to a crash - stocks are a volatile, risky, long-term investment.         

To summarize:

Your first premise: True but not actionable via equity mutual fund investing.  Managers chase performance, slow down their returns relative to the indices by holding cash even in the best bull markets, and are reluctant to build significant cash stakes until they have already experienced significant losses.   

Your second premise: False, unsupported by statistics, and contrary to your argument.  You don't tell us what percentage cash your managers are holding or when they developed this holding.  A major reason for the values in a bear market is outflow from equities.   

Your conclusion: True but unrelated to your premises.  You should hold your funds because you don't know how to invest in equities, you've already taken the losses of the last year, and at some point a bull market will come along and rescue your managers.  If your investing rationale is accurate market timing by fund managers in a world where they're under pressure from investor outflows and a daily performance focus by the media and their bosses, then I would love to have the opportunity to sell you the Unicorns and Fairies Fund (UFFMX).  Our investing thesis is that Unicorns are a big growth industry because no one else is investing in them, and Fairies have been a stable performer over the last 1,000 years.  If you pay us 1.5% fees per year regardless of performance we might be competent enough to not lose any of your money!