Yes, we actually started by making making Enterprise Edition actually open source. When we announced there would be a proprietary part of GitLab people mentioned that Wordpress plugins where able to make it work with an open source license. It was a comment on https://about.gitlab.com/releases/2013/08/22/introducing-git... but the comments there seem to have disappeared. So instead of making it proprietary we licensed it with an open source license but without offering a download, you had to pay to get access to the source code (this is similar to the Wordpress plugins and also not unlike Red Hat Enterprise Linux updates).
We were afraid that people would put up a mirror with the paid code, this didn't happen. But our customers told us that it was hard to justify paying for open source code, they got lots of questions from their managers. So we switched to making the additional features proprietary.
We tried charging for support but it is hard to make enough margin to be able to invest in the things we wanted (scalability, security, library upgrades, easy of use, etc.). People tended to cancel after they didn't use support for a year. I believe that most companies charging only for support are tempted to make the product harder to use to increase the need for support. More about the business models we tried can be found on https://about.gitlab.com/blog/2018/11/09/monetizing-and-bein...