Any large software companies with no PMs that are doing well?

There are lots of different kinds of PMs. Many (ok, a scant few) aren't Agile monkeys or obsessive about bogus engagement stats.

My company is a not for profit research organisation. When a product manager could be considered, it's usually time to do a spinoff and to keep focusing on what's fun.

Some companies are not product driven.

I worked at a marketing driven company, where marketing would work with sales and customers to figure out what was needed. Marketing would then pass that down to project managers who managed UX and engineering projects.

The work that product managers do is usually present in a company, but it's not always consolidated in a single person. In this example, it was spread out among marketing, project management, and UX.