I know that it isn't possible to change the inode count of an ext filesystem after its creation, but I haven't been able to find any explanation on why it isn't.
Can anyone enlighten me?
Why? Because no one has written a tool that does it. And that's probably because it's a not entirely trivial change to the filesystem metadata.
There are other issues like this; for example you can't resize ext4 to >16TB. That needs 64bit structures which aren't used by default.
Same with other filesystems, for example you can't shrink XFS.
None of these things are impossible, but it seems that no tools exist to do it either, at least not directly. Someone would have to develop them... and that usually requires in depth knowledge of the specific filesystem.