I suggested keeping 'past', and he brought it back -- although this might have been as much for layout reasons as for any persuasiveness I had. Personally I used 'past' much more frequently than 'web', but I'm sure he'd listen to arguments for 'web' if there was a significant contingent who misses it. Write him email if you don't get a response here.
Anyway, if you want it back you should probably send an email to hn@ycombinator.com too. Two people emailing is better than one.
1) When browsing I have 'Show Dead' on and after reading the front page of HN I head over to the 'New' section and take a look at the submissions there. Often there are articles in that section that are just direct copies of the original article from a different site that have been posted just to drive traffic to their (the submitters) own blog. Hitting 'Web' makes it easy to spot those and where appropriate suggest linking to the original source either via an e-mail to HN or more rarely in the comments.
2) Some of the submissions on the 'Newest' section are in a foreign language. Hitting 'Web' allows me to either just skip it or hit the ‘Flag' button.
In these sorts of edge case instances knowing the source origin of the article (if any) allows me to express a more nuanced opinion or to decide when and if to flag a submission. Note - I don't (didn't?) use the Web button for any and all submissions I read or comment on but with the ones that I did use it for it allowed me to decide whether to engage, skip or flag with a single click.
I accept that the way I used the 'web' button seems to be different from the way others used it and few people some to use it at all so I'm not too fussed about it being removed.
I have great admiration and respect for the way the mods run HN so I'm not gonna fire them an e-mail over this but perhaps others DO use the web button and can chip in with their own feelings / use cases in a single place rather than the mods having to deal with several e-mails. Also, leaving it here allows Dan & co to link to this submission if/when it comes up in the future.
Direct motivation for the removal,
> That part I can help with: HN has a policy that paywalled content is okay as long as it's a soft paywall and there's a way to bypass it. AFAIK that's what the "web" button is there for, even if in my case it has not worked even once.
is wrong, though. While most sites have closed the loophole where visiting with a google.com referer header bypasses the paywall, Google still caches a full text copy if Googlebot isn't paywalled, and the cached copy can be accessed through "Cached" in the dropdown menu next to a Google search result. That works for many paywalled sites including Bloomberg.