"..claiming that such genres such as pop, rock and classical arent the 'peoples music'- people made this music, and therefore it belongs to them."

Well, Otis, I see your point, but "people made this music, and therefore it belongs to them." is something between a cliche and a tautology. It is very close to the old "I ain't heard no horse singing it" line.
   The point is not to debate whether some particualr word should be defined precisely or not... the point is that categories exist, and some people make special efforts to find, buy, listen to, collect and play & sing...varying types of music. There ARE people who listen mostly to orchestras playing 'classical' music & opera...so they need a word for it when they go to the music store or search for it online.
   Obviously, the same goes for Hip-Hop, Rap, Bluegrass, 'Country', Dixieland jazz, Heavy Metal...and many etcetras! Some people, like me for instance, discovered in the 50s & 60s a type of music which had most of its roots in older music & song that was traditionally played at home for fun and passed down orally for sometimes hundreds of years. As this music was gradually recorded and talked about, the terms 'folk' and 'traditional' were used to refer to it. It wasn't a clear, precisely defined area, but for 30-40 years it was pretty clear what was meant, even though the edges were often fuzzy!
Now, we often STILL need to refer to those old songs, tunes... and the people who kept that music alive. *IF* people keep crowding new genres and variants under the umbrella of 'folk', the word ceases to have much use at all! I can no longer say "I like 'folk' music" and be sure you will know what I mean.
I do NOT care much for 'electrified' folk, or most 'singer/songwriter' stuff...with certain exceptions. So... after most of my early years being able to say "I like 'folk' music, what am *I* supposed to do now to avoid spending my money badly when I see a 'folk' concert or festival advertised?

   I repeat, as I have repeated in this forum for over 10 years...if a word is used too broadly, it begins to have little meaning at all... The reason we HAVE different words & phrases is to differentiate between various categories..in places like stores and web sites and concerts.

   I am quite aware that I have essentially lost the battle to preserve 'folk' to mean music with a certain set of characteristics...the word is just too short, simple & useful.
But maybe, in little corners of the world, I can remind a few 'folks' what we are really dealing with.