I use a wildcard certificate for my home infrastructure. For all the talk of hiding, though, it's wise not to count on hiding behind a wild card. Properly configure your firewalls and network policy. For the services you do have exposed, implement rate limiting and privileged access. I stuck most of my LE services behind Tailscale, so they get their certificates but aren't routable outside my Tailscale network.
Doing something similar on AWS right now, what do you mean by leaking service usage? What is ACM exposing? I assume the “fix” for this would be to host your own CA through ACM?