But that makes operational expenses go up. For instance, now you have to tweak the Nginx config to support the service that normally lives on that machine and the new system. And you still have to write and maintain the web service driving it (which may not be hard, like a Flask app with a single route, but still more than zero). And you still have to maintain the server itself, which should involve regular OS updates and any work you have to do to automate deployment of the web service, unless you really like doing all that stuff by hand.
Or you can upload a single function definition to Lambda and let it do everything else.
Again, I wouldn't use Lambda for everything, but I'll gladly let it handle the stuff I won't want to bother with.
On the other hand, you're probably all set up to do that already. It's no big deal. Introducing a new tech requires training, new deployment procedures, new documentation, etc., and now you probably have a one off component out there. There's a line somewhere, but if I were just adding a webhook for log events I'd throw it on a server I already have.
It's almost never about server capacity. It's usually about who's maintaining them, who controls the updates and versions of software on there, and which dept the server's billed to. All stuff that's reasonable for things of a certain size, but unreasonable for things too small or big to fit the process will.
I would love to see a study of how much IT spending in general is just for tools to work around corporate bureaucracy. I suspect the figure would be staggering.