Ack, you mentioned the F-word - take cover. That really is the heart of the problem here. 'Feudalism' these days is a pop-history oversimplification of the Middle Ages, and in trying to encompass the incredibly diverse structures of Western Europe over a time period of several centuries, utterly fails to do so. The first thing we're going to have to do is discard this notion of 'feudalism', period. If you've got some time to read, the Middle Ages section of the FAQ leads off with four links about Why The Concept Of Feudalism Is Problematic.

Now, that little wrinkle aside, another thing to mind is that there's a few things off with your understanding. Namely, just how much military power the nobility contributed. It's certainly a substantial contribution - but not 'all', and certainly not to the extent that the king 'had no real teeth'. To answer this, we bring forth a bunch of threads from my Medieval Armies Compilation.

Mainly because there's a lot of posts on it, this first set focuses on England:

• u/Rittermeister examines how Anglo-Norman England did it;
• Rittermeister and u/MI13 examine the familia of a lord, expanding on one of Rittermeister's points in the previous answer;
• MI13 also further covers how England did it with an important change in method;
• and u/Hergrim also looks specifically at 1100s-era England.

Don't stop just yet, more links in next post because argh tag limit.