There's really nothing "oddly pig-headed" about not allowing 3rd party system level apps to run on iOS. Can you really not see why? Part of iOS's security and stability is because it doesn't allow 3rd party drivers or system level "mods" to be downloaded and installed- sure Apple themselves can come with some nasty bugs from time to time, but you'll never see someone running Safari that's been taken over by 9 different toolbars or constantly grinding the disk to a halt loading adware. And you won't have people installing a 3rd party keyboard that logs and sends everything that's typed to some crafty criminal's server.
I do think Apple needs to do something here, but I doubt it will be simply opening up the app store to random 3rd party keyboards. Either Apple themselves should simply purchase/license another keyboard option, or they should make a highly curated program for incorporating them, like the MFI program for 3rd party hardware.