So, RMS set out to put together a w/holy free operating system, or die trying (of old age, presumably).
Now, you know one of the decisions of the project was to use whatever Free Software was already available to do the job, rather than writing it all, right? Such stuff as sendmail, X11, TeX, and even Mach (intended to be used as the lower layer of HURD) were already Free back then, and GNU was happy to use them.
Now, what if RMS had found out that say TeX contained some non-Free bits? Turn a blind eye to it wouldn't be honest, so they'd have to be (i) removed, and (ii) reimplemented, as people found the needed and the will to do so.
You'll notice that (ii) necessarily follows (i), even if they're mostly simultaneous, say, because some of the bits are absolutely trivial to rewrite and release under a Free Software license compatible with any other pieces it gets combined with.
However, the harder it is to reimplement the bits, the longer the time is likely to be between (i) and (ii). In any case, (i) can be a great motivator for someone who was comfortably unaware of the non-Free bits.
Unfortunately, the blobs in Linux are of the harder type to reimplement, because most often information is not available. There is progress, albeit slow. In the mean time, the Free Software community needs a Free kernel, and Linux is growing less and less Free, so Linux-libre fits.
And it fits perfectly well in the original plan for GNU: use Free Software that is already available, and implement whatever else is needed to get a w/holy Free system that people can use. If using Free Software that is already available means cleaning up nearly-Free Software, so that it becomes Free, so be it => Linux-libre.
It would be just silly to reimplement stuff from scratch, as some suggested, and it would be nonsensical to wait until all the remoevd non-Free bits are reimplemented before letting people use what is Free and perfectly usable.
Sure, you may find one component or another here and there that will adamantly refuse to serve you, but as someone else pointed out, you can always replace the component if you wish to. (and you can find a freedom-friendly replacement, and you don't find out that the hardware system vendor doesn't limit the system so that it refuses to function if you replace the WiFi cards or the hard disks or any component whatsoever with something not supplied by their salesmen or authorized repair shops)