In case it helps someone else, as I stumbled into this thread while investigating this problem:
@aardgoose already explained it perfectly but I would like to insist to give it more visibility. If the GPU is busy no matter what the ‘native’ WebGL call is then it will show in the chrome dev tools performance profiler as the operation taking the long time. It’s not that this specific operation (getProgramInfoLog) takes a lot of time but that when it’s called the GPU was already maxed-out doing something else and any new sync operation involving it will be delayed until it finishes.
That’s why when removing the getProgramInfoLog call then the getProgramParameter appears as the new long operation, it just took over because the GPU can’t handle the load.