Probably most people would deem the risk negligible, but it’s still worth to mention it, since you should evaluate for yourself. Regarding the central machine: the certificate must not only be generated or fetched (which as you said probably will happen “at the center”) but also deployed to the individual services. If you don’t use a central gateway terminating TLS early the certificate will live on many machines, not just “at the center.”
You are absolutely right. And deployment can be set up to open up additional vulnerabilities and holes. But there are also many ways to make the deployment quite robust (e.g. upload via push to a deploy server, distribute from there). ... and just by chance, I've written a small bash script that helps to distribute SSL certificates from a centrally managed "deploy" server 8) [1].
