I agree on security issues, and making the path depend on an environment variable/per-user config file would be opening a new can of worms.
However, an issue I have is that while you can configure that path system-wide, there is no way to control it per-user, or with a finer-gained approach. You can probably use mount namespaces to shadow a ~/.ssh with another config, but that seems overkill.
I admit I have no practical use cases for this right now (though I probably did in the past) besides "uncluttering $HOME". As for hunting the config files, those would reside in ~/.config/ssh by default. I personally find it more irritating when a program picks a random folder instead of conforming to the spec (and if I set the environment variable to somewhere else, I then know where it is). Go hunt trough ~/{.program,.program/conf,Program/conf,Documents/Program/conf,Documents/My\ Games/conf}, or countless variants I experienced. Thought it is admittedly a much smaller problem with better-established programs such as openssh.