The descriptions are most useful for people who don't already know our tag set. Hiding them is likely to increase the rate of mistagging.
Tags are ordered by frequency. If you're a new user you should be looking first at the most-frequent tags; unless your question is obscure you're probably going to want something on the first page or two. (This generalization might not apply to SO with its many languages and frameworks.)
The tags page has a search box, and as soon as you start typing the list is filtered -- so if you don't see what you're looking for immediately, type a few characters and see if that helps. The search box contains the hint text "filter by tag name"; does that need to be more obvious? (It's light gray and I admit I missed it
Finally, if you want to browse by name rather than searching/filtering, you can use the "Name" tab and then jump around in the pages to try to hit the right range. But filtering is going to be easier.