None of the FAANGs block personal projects from staff who are productive enough in their primary responsibility

What if the "personal" project is like "introduce this new tooling to the team, get it integrated into our CI pipeline"?

Anything that introduces new technology or has the potential to require some time from other teams (Devops, SRE) I can see running into organizational roadblocks in the final stages of the project, even if the individual is free to start the experimentation and justification steps them on their own.

I think you're referring to "gatekeeping." If the employee, for instance, proactively fixes a bug or resolves some technical debt, it's possible another team member might try to prevent it from being merged. Their reasons might seem non-objective and rooted more in the fact that they weren't involved in the change, or involved in the decision to make the change. I've ran into this.

It's easy to be discouraged and, in the event this occurs, stop trying. That said I think this is the wrong thing to do. Instead I view this type of scenario as a chance to convince my teammate of the value I'm adding and the rationale behind the change being made without being explicitly planned. It's hard work, and sometimes involves some long, strained conversations with your team mates. That said at the end of the day you just might encourage that individual to proactively solve these types of problems. This will probably make that person happier as well, and unlock additional productivity for your team.

The hardest part of software is the people part :)

If they're willing to do the integration and support work on their own, then it shouldn't be a roadblock, and they should be able to prove the impact that it offers to other engineers and be rewarded if they did all of the work.