I used my Google Location History as part of an alibi with the police (it never made it to the courts). My guess as to why that was successful despite the obvious flaws was:

1. The crime occurred in another city about 3 hours way, so poor granularity or precision really didn't come into play.

2. The crime itself was a hit and run on a road worker. Not something you'd generally believe to be premeditated where I'd have thought to have a friend haul my phone around town to provide an alibi.

It's not the best alibi since your phone isn't physically attached to your body. Someone intending to commit a crime can easily drop their phone somewhere else to conceal their true location.