Yes, in my commuter-heavy locale, employers often subsidize transportation and parking costs.

When working on my own, I charge clients for travel costs or build it into their pricing.

I don't, because I'm not at work while I do those things. I'm willing to take responsibility for getting myself to work; but I don't think it's fair that I'm currently loaning my employer some free square footage in my apartment that's dedicated solely to their economic activity.

If they're paying you, isn't it dedicated solely to your economic activity?

In general things like public transport ticket subsidies and work cars are not that rare here. But the employer also saves rent, utilities and maintenance when someone is working from home compared to that person requiring an office.

Where is here? AT least in the USA, cars used for commuting are almost never covered. If it's a car used for the job itself, then it is.