I honestly thought about covering a few ideas in the post, but decided it was off topic. The service meshes do include some rudimentary key generation and distribution code, which is nice to not have to build yourself. The simplest thing, if you're deployed in k8s or similar, is cert-manager + a CA + code that reloads keys when the secret is updated (pretty easy to write). This has downsides (good luck when your CA expires!) but it is easy and does keep itself functional. Cloud providers also have a service like this, which protects the root key with their own IAM (and presumably dedicated hardware); it's definitely a route you'll want to look into.
What's missing are a bunch of things you probably want to check before issuing keys; was the release approved, was all the code reviewed before release, is the code reading the foo-service key actually foo-service? That involves some input from your orchestration layer; i.e. an admission controller that checks all these things against your policies, and only then injects a key that the application can read. (Picking up rotated keys becomes more difficult, but this might be a good thing. "If you don't re-deploy your code for 90 days, it stops being able to talk to other services" doesn't seem like the worst policy I can think of in a world where Dependabot opens up 8 PRs a day against your project.)
This all has the downside that it doesn't really prevent untrusted applications from ruining the security; a dump_keys endpoint that prints the secret key to a log, nefarious code checked into source control but approved (perhaps due to a compromised developer workstation), etc. Fixing those problems is well outside the scope of a service mesh, but something you have to have a plan for. CircleCI didn't! Now you read 3 blog posts a day about how they got hacked.
Anyway, not sure where I was going with this, but application teams need to consider their threat model and protect against it. Security isn't a checkbox that can be checked by someone that didn't write the code. Sure, you can get all sorts of certifications this way that look nice on your marketing page, but the certifications really only cover "did they do the bare minimum to look kind of competent if it was 10 years ago". If you have sophisticated adversaries, you're going to need a sophisticated security team.