TINA just tells you what's happening, not whether the players are making the right moves. If you are a pension fund manager, then every month you get a bunch of money which you need to invest right away; the choices are stock indices at maybe 4-4.5% (current earnings yield+growth), or cash and bonds at negative real rates. (IMO negative real rates changes the players' psychology a great deal compared to rates which are extremely low, but still positive)
At some point it will clearly not make sense to invest in stock indices - Japan reached this point in 1989 with large caps trading at 50x-100x earnings. However, Japanese players could always invest abroad without totally swamping overseas capital markets. If U.S. capital markets get to the point where real yields (including stock earnings yields) are negative across the board, the consequences are totally unpredictable but should involve lots of fireworks.