Second, ports and portage have support for and networks of mirror servers that keep copies of software available through these packaging systems. It's trivial to switch if one of the mirrors goes down. For pip, gems, or npm you need to plan ahead for the problems and deploy your own package cache, from what I know.
Third, I was using Gentoo with one of these "battle tested systems that work well in production" for several years. It was doable, but it wasn't pretty, could lead to breaking software after updating some random deep dependency (if it was recompiled with different flags), and generally required more work and attention than APT would, all that for very little gain (if any gain at all). Oh, and it ended up working with binary packages, after all, I just needed to compile them myself instead of having a half an hour downtime of production MySQL because it needed to get compiled (which could fail, leaving me with no working database installed).
I bring that up to highlight some of the wrong assumptions you make. You make several needless assumptions and use those to draw funny distinctions between things. I am not even sure of the point anymore.
likely any of these systems could be used in a variety of environments for a variety of purposes.
And I have yet to hear that port and emerge are incapable of doing dependency resolution. They're battle tested systems that work well in production environments.