It's actually a lot easier, unless you have next-to-zero traffic, to ask _them_ to take an action that puts the info in your inbox, rather than dig in logs, which could have that specific user's information buried amongst hundreds of other entries. It's a time-saver.

What if you have insufficient logging (Heroku sans a decent logging plugin, for instance)? What if you built the thing, but it's hosted by a third-party that limits log access? What if you want some non-technical or not-that-technical person to handle the issue?

As hackers, we tend toward "do-it-yourself", but there are a lot of cases where that isn't practical or economical.

If you can't quickly identify your client in your logs you will have bigger problems.

Sure, but the usual support rep has no log access. But using a good knowledge base, he can answer things like "Flash 9 doesn't work" without tech assistance.

Why doesn't the tech support rep have access to the information he needs? The data is in the organisation.

Because he might not be qualified to read it and providing an aggregation of said data in a consumable form is too much implementation work?

In some organizations, he is not even allowed to read operational data without pre-screening.