Assets managers compensated based on AUM have little incentive to reduce or liquidate equity holdings and move into cash or fixed income that pays so little, clients would just remove those reallocated $'s out of the accounts to avoid the Fees.
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I like your choice of the word "phenomenon", I think it is part of a bias that promotes higher equity market prices which may not reflect intrinsic valuations
To the extent that equities fund managers take larger position sizes than they otherwise would to stay out of cash, the effect on prices is probably marginal. Usually when an equities fund gets too big for the strategy to work the managers tend to raise fees and/or close the fund