Has there ever been any petition in the UK that has achieved any effect other than "thanks we'll think about it"?
It's the equivalent of those door buttons in elevators. "Give them something to do when they're restless."
Online petitions are useless for anything beyond harvesting a list of potential donors.
The value in a petition or protest is in demonstrating commitment. If you’re willing to fill in a paper form and/or show up somewhere inconvenient, you’re might also be willing to phone bank (and petition for) a primary opponent.
Online petitions do none of that. If an issue has lots of online petitions and nothing else, it’s almost a sign that its base is electorally useless.
A slightly cynical take, but accurate none-the-less.