Removable valve cores serve a couple of functions. One, you can put tire sealant in the tube. Two, you can use the better valve extenders with them.

That said, we had our own problem with a removable valve core Saturday. Flatted front and back. We were riding Zipp 808's and one of the replacement tubes didn't want to play well with the Zipp valve extender.

So I got the bright idea to remove the extender from the front wheel,and swap it out in the back. Unfortunately the valve core came out with it. Ended up going through 3 C02 cartridges, and had to use a mini pump which then lead to breaking the valve extender off below the rim.

It was a complete comedy of errors.