If the Cosmos was teeming with "life, Jim, but not as we know it," wouldn't we still see the evidence of its effect on its surroundings? In accordance with the principles of Conservation of Energy and Entropy, life needs energy to survive, at least while it's active (not in suspended animation). So far we have not seen any gigantic swarms of space-borne organisms gobbling up all the sunlight they can find (which is good luck for us). While there still may be microbial life on Mars or some of the other planets, we haven't seen any verdant forests of trees with ammonia sap, etc. on any of the planets we've had a close look at.
Nor, when we look out on innumerable stars and galaxies, do we see any evidence of Dyson spheres (artificial or natural) or anything else that looks out of equilibrium from the perspective of non-biological physics. That is, no equivalents of Earth's oxygen atmosphere, which would not exist without plants continually regenerating the oxygen supply. It all looks exactly like it would if it was not populated.