Because if you are running a hedge fund or institutional fund and stocks keep going up after you've sold them -- which could well happen -- you run the risk of having some major investors cash out because they're angry about missing out on the profits they would have made had you not sold. If that happens, the income you get from running your fund, which is based largely on its size, will go down.
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The seemingly irrationally rising market also poses an interesting problem for money managers who, unlike Buffett and Abel, need to worry about investors fleeing if they begin to replace stocks with less-risky investments -- and reducing managers' income as a consequence.

I think there is a subtlety to this dynamic mentioned in the paper I referenced up-thread which I never fully appreciated before: mostly, they don't because they can't.

The great majority of "new" investment into equities globally in recent years ("new" in the sense of not being funded by selling a different stock) is done via managed funds or portfolios of one sort or another. A substantial majority of their managers have absolutely no flexibility in their stock allocation. Either 100% because they are a long-only stock fund, or a fixed percentage because of some inflexible target mandate, even if that mandate is long/short like a 130/30 fund. In that situation, the managers might be screaming for permission to have fewer dollars allocated to stocks, honourably and without any regard for their personal career risk, but their hands are tied. Every time a dollar comes in the door, they MUST buy more stock, no matter what price it's at.

Further, from whom are they going to buy it? With so much of the equity held in portfolios with fixed allocation mandates, it takes a very big bump in price to tempt anyone to sell. Big enough for fixed-allocation funds to get out of balance. So, we see irrational bull markets--even if almost every participant knows it's irrational and wishes not to participate. They are doing it because the DCA crowd (among others) has hired them to do it.

The paper is interesting because they claim to have found a way to put an actual dollar value on the amount that the prices have to go up when "new" money arrives. They estimate that each new dollar into equities (not coming from sale of other equities) raises aggregate equity market cap by $3-$8 on average, around $5 as a working hypothesis / rule of thumb. A pretty extreme amount, if true. They estimate that stock buybacks in aggregate have a much smaller effect, for the simple reason that there is also a whole lot of stock issuance counteracting it.

Jim