I haven't made my first commit to a public Github however, it seems to me you can easily keep your streak with minimal effort. Why not just stash a small commit during the week and have a cronjob commit it for you on Saturday and another Sunday?
Maybe you code 18 hours M-F. Is a guy who codes 5 minutes 7 days a week cheating because he gets a streak and you don't? Whose to decide if he is gaming the system by barely contributing.
But I think your second paragraph addresses the real problem: contributing 18hrs/weekday and contributing 5mins/day are both legitimate open source contribution styles. But the "streaks" metric removes all subtlety -- how many contributions are they actually making; are the changes meaty or trivial; do the changes break CI; do the changes address Issues in their respective repos -- and so I don't believe it is a helpful metric to display.
Personally, I believe it does more harm that good, by encouraging people to maintain streaks even if doing so actually decreases their true productivity or happiness. But no matter how much or how little harm it does, I think it is hard to argue that it does much good, since it is such a high-level distillation of complex information.