I'm not quite sure why you think pointing out someone's confidently incorrect claim that containers do give you reproducible environments means that I fetishsize anything?
But if you genuinely want to know why reproducibility is valuable, take a look at https://reproducible-builds.org/.
I was quite happy to see that Debian and Arch have both made great strides into making tooling that enables reproducible packages in recent times. It's probable that, because of efforts like this, creating reproducible builds will become easier/possible on most Linux environments, including traditional container workflows.
For now though, Nix Flakes are much better at enabling reproducible builds of your software than traditional containers, if you can suffer through Nix not being documented very well. This article covers some more details on different build systems and compares them with Nix Flakes if you want more concrete examples.
FWIW, I think that containers are awesome, and using them for dev environments and CI tooling solves a lot of very real problems ("it works on my machine", cheap and easy cross-compilation for Linux systems, basic sandboxing, etc.) for people. I use containers for a lot of those reasons. But if I need to make something reproducible, there are better tools for the job.
I've packaged a CLI that I made as a flatpak. It works just fine. Nothing weird was required to make it work.
The only thing is that if you want to use a CLI flatpak, you probably want to set an alias in your shell to make running it easier.
I'm not sure why more CLIs aren't offered as flatpaks. Maybe because static linking them is so easy? I know people focus on flatpak sandboxing as a primary benefit, but I can't help but think of static linking was easier for bigger applications, it wouldn't be needed as much.