I think this is really just a naming problem. The Apache Software Foundation was founded for the Apache webserver, but today they have hundreds of projects unrelated to that. The same is true for the Linux Foundation.
Good point. In a sense, foundations have to appear much more interesting than they are nowadays. Developing an OS kernel or a web server isn't appealing to newcomers, so I guess there should be alternative pathways to that. There should still be alignment in behaviour to the identity the entity claims to be. Or we just could have the Whatever Foundation. So, are these other projects in any way related to the development of Linux kernel or not?