Earlier quoted context omitted.
The point of physical petitions is they're hard. Showing a politician a few thousand names, with verified voter-registration statuses, who wrote out their addresses, and maybe copied a single sentence expressing their support for your cause, is much stronger than a million people who clicked an Internet button. The former can be organized to the politicians benefit (or against him, to his detriment). The latter proba…
I would tend to take the cynical view that the point of petitions in general is that it lets people feel like they're making making their voice heard and acting as a pressure relief valve of sorts for all but the most serious of grievances. Most protests today fulfill the same purpose.
Why? Off-season elections, which most of these politicos must win to keep office, are not games for numbers. They're games to motivate people to inconvenience themselves by voting.
Remember why politicians like PAC and campaign contributions. They spend that money on turning out voters. If you can turn out a bloc of potential voters, or people whom you can reasonably claim are upset enough to vote against them, you'll catch attention. The active minority wins against the disinterested majority. Internet petitions represent the latter; hard petitions and protests high in repeat attendance demonstrate the former.