That should be a choice up to each person with a sensible default. You could let users define home/work zones where no data would be shared. You could add a bit of delay to the data transfer to be able to say "don't send anything from the first and last X minutes of moving".

OSM is full of GPS traces volunteered from thousands or people. The NYC taxi data set is not that different and includes exactly the data you describe.

I very much find the taxi data a inconsiderate breach of people's privacy as I doubt they were aware that this data might become available. But I consider volunteered detailed trace data perfectly fine and actually necessary for a open platform as you cannot reproduce results otherwise.