Light bikes might actually matter if you're racing. A couple hundred grams up a long hill might be worth a few seconds, which might be the difference between keeping with the lead group and getting dropped. This weight is exactly the same if one can lose it off of their body, but some racers are at the point where losing weight isn't possible without compromising other performance qualities.

A couple of seconds over a 20 minute climb isn't even going to be noticeable if you're just riding and having fun. People who think that their bike "feels" lighter after some purchase are just trying to justify that purchase.