I work for a product with big numbers too. We have humans reading the support queue (with a lot of engineering to prefilter and group for bulk replies and what not). People may or may not like our support, or may complain it's not as good as it used to be, but it's there.

Frankly, we couldn't have as many users as we do without a human connection in support. Users tell us what we're doing wrong, and what we need to do that we're not doing, and where we need to improve --- but only if you listen to them.