I see little difference between searching for evidence of time travel on the internet and searching for evidence of pink unicorns on the internet. Current theory predicts that we should not find evidence of either one, nor any evidence of ESP, telekinesis, or a zillion other phenomena. So searching for evidence of these phenomena and failing is about as interesting as searching for evidence of anti-gravity by dropping a few dozen apples and failing.
Confirming common-sense "obvious" results is actually one of the important things science is for. Sometimes it turns out those obvious things aren't actually correct and nobody had bothered to check.
When the results indicate that established theory is not correct then yes, that is obviously important. But confirmations of well established results are only important when they test the theory in previously untested realms (e.g. a measurement that tests general relativity to a greater level of precision or in stronger gravitational fields than previously performed). Confirming the non-exitence of time travelers by failing to find evidence for them on the internet is like confirming the non-exitence of leprechauns by failing to find pots of gold at the ends of rainbows.
