As somebody who is self-employed (doing freelance, contract, and consulting work) my perspective on this might be a little different since I'm my own “employer” as much as any of my clients are :D
I have always cared about design and helping people, so while I was trying to use my design skills to help people (build a Ruby on Rails web app) I ran across a problem with responsive design.
I had a few choices:
Exploring any of the options would have helped me. Option 1 means more paid hours of labour for me, Option 2 means less paid hours of labour, but possible some hours of tool-building, and Option 3 means after it's built, everyone in the world will have less billable hours but also be able to build more things with the same time + resource (or build the same things with less time + resources). I prefer doing work where the employee's interest and the employer's interest are aligned (Option 2) but it can be even better if the same work that benefits you and your employer can also benefit the whole world (Option 3).
So I took Option 3 and started the research that would lead to the EQCSS project! Once I had figured out what we needed, instead of having my client pay for it and own the plugin, I hired a developer for about 2 weeks of labour to help me write the first version of the plugin and released it as open-source. Now me, my clients, and everybody else in the world can benefit from the same solution.
As time moves on, having that side project has saved the day almost once a month for something we need to do - this has only energized me with inspiration to build even more side projects. If EQCSS was my first CSS-related plugin in 2015, I just released my 20th CSS-related plugin less than 2 years later!
So… What is the value of a 'side project' for the employer?
I could try to pitch all this 'tool building' as a necessary part of the work I charge to clients, but then I feel like I wouldn't be able to open-source it and release it in a way that everyone (including my clients) can use it and benefit from it. So I believe strongly enough in the importance of these 'side projects' as my own employer to fund them myself with my own unpaid time, or even by paying money out of my own pocket to hire developers to help me build the things I can't build myself.
If you're an employer and not sure about the value of these side projects, I question how you can afford to not to do them!