No, it (or they) is (are) not essential. What it (or they -- they are usually plural, one for each note) does is precisely determine the free length of the string and the location of the strings, both horizontally and vertically, at the pin board end -- very close to where the hammer strikes. If they are not present, there must be some other piece -- perhaps a sharp edged bridge -- between the pins and the free portion of the string which serves the same purpose.
Like so many other mechanical widgets, it doesn't matter what you call it or even whether a specific widget is there or not; what matters is whether or not there is something about the construction which accomplishes the purpose.
Not to be confused with a capo d'astro bar... which some pianos (e.g. Steinways) have on the treble strings (in an A, from the C above middle C up). This is between the agraffes on those strings and the hammer point, and effectively determines the main speaking length of the string, rather than the agraffes doing that. The interesting part of this bar on these pianos is that the length of the bit of string between the agraffe and the capo d'astro is a particular fraction of the main speaking length, and when the note is played it vibrates too, but at a much higher frequency and, supposedly, adds to the brilliance.
Topic: Piano and Agraffe..