Being able to count the beats in each measure is a valuable skill for many (any?) musician. (In my opinion) It is incredibly useful in figuring out rhythms, syncing with the drums (or explaining drum patterns to drummers ;-), and often simply in working out songs with your band mates. In other words, it's part of the lingo that goes with being a musician.
I think that PJSShearer's point (and I agree) is that when you have achieved sufficient proficiency at sight-reading, you no longer need to count in order to figure out rhythms. It's very much like learning to read. When you are first learning, you need to think about each individual letter in every word. Over time, you begin to recognize words as words rather than as a collection of individual letters, but you still need to think about each word in the sentence individually. With more experience, you can start to read sentences and understand what the writer is trying to convey without having to think about the function or meaning of each individual word in that sentence.
Reading music is a similar process. Counting is part of the process of learning how to take individual notes of various durations and figure out where that note is played within a measure. In the same way that you stop reading individual letters and start recognizing whole words, you eventually learn to look at a measure of music and understand where each note is to be played without ever having to consciously think about the individual beats in the measure.
Take the following figure, for example:
Someone just beginning to learn to read music might work out the measure like this: "The first note is an eighth note, so that gets half a beat. The second note is a quarter note, so that gets a full beat." And so on.
A more advanced reader might be able to look at that measure and, without having to consciously think about eighth notes, quarter notes, etc., recognize that it is played "
one and two
and three
and four
and one two three four." That person understands the duration of each note written on the page, but still needs to count to himself to be able to play the notes in the right place.
People who can truly sight-read have reached the point where they can look at my example, and just play it. They don't need to consciously think about which notes are quarter notes and which are eighth notes. They can look at the measure as a whole and recognize which notes fall on the upbeat and which fall on the down beat, and play the measure without ever consciously counting the beats.