No, you can grant yourself this inside an unprivileged user namespace. `unshare -Ur capsh --print` lists the capabilities inside a user namespace and demonstrates that it has both CAP_SYS_ADMIN and CAP_NET_ADMIN.
Almost all distros allow unprivileged user namespaces, and in my opinion this is the right decision, because they're important for browser sandboxing which I think is more important than LPEs.
I don't think namepsace CAP_SYS_ADMIM grants you access to write non namespaces sysctls like modprobe_path
You're probably right, but that seems like the less important part of this. At that point you've already got an out-of-bounds write. Another comment speculated that you could use PageJack as an alternative exploit path once you have that primitive: https://news.ycombinator.com/item?id=48069623