The IA is a great project and all, but it's not really the same as the Library of Congress. LC has to be sort of an indelible record of the doings of government and the literature of the day. The scope is big, but it's well-defined.
The IA is a moonshot effort at capturing everything, which is another way of saying it's more important to capture more things than it is to capture a given single thing well. It's interesting and important, but it's anti-library in a way, rather than being an enhancement of what libraries do.
Not to mention, I don't really believe IA is a pinnacle of digital library engineering by any means. I've heard tell of digital signatures that have shifted over time, for example.
I think Mr. Kahle has come to represent "forward thinking" in terms of providing library services in a digital age in the technology world, because he comes from the Valley and founded a successful internet property and whatnot, but that doesn't mean there aren't prominent technologists that come from the library world rather than the tech world who aren't also capable of pushing LC forward on the digital front.
The Library of Congress, like every library in the world, needs to not only get serious about digitization of content and archival of web content, but also about providing access to that information for the public.
This not only requires the right kind of technology for data archiving (which the Internet Archive has developed and used successfully), but it also requires a step forward for the nature of things like HTTP, and how we federate and distribute data. With the right technology, we absolutely can and should archive as much information as we can to preserve our true history for future generations, not just the "New Books" section of Barnes and Noble.
I've been doing some work on that front, and Brewster was right there advocating for it (http://brewster.kahle.org/2015/08/11/locking-the-web-open-a-...). When it comes to getting things done, I bias towards the people that show up to do the work. Brewster showed up, but I haven't seen any "digital library world" people around lately, except for when they tried to lock up Aaron Swartz for opening up JSTOR, a company making a profit off the public funding of research by locking the public out of the information it paid for. That's not the future of information, and that's not how things are going to be. All that is is a data cartel that's run out of ideas working to push out competition.
I think the only relevant question here is "does Brewster actually want the job?", but I think he's perfectly qualified for it, and there is not a single person on the planet that is better qualified for it.
[1] http://ascii.textfiles.com/
[2] https://en.wikipedia.org/wiki/Jason_Scott
Edit: Oh, I guess BK is an IA person, so he knows Jason Scott very well :)