Look at the MLS as a classified ad.
If you had a lawn mower for sale, you can list it online, in the paper, sign out front of your house (with HOA permission of course), etc. It is up to you how you want to get the word out that your lawn mower is for sale. Same thing when selling a house, the MLS is just the accepted place to go looking, agents make it easier on themselves and other agents to list it all in one place. So say you wanted to sell your lawn mower, if there were a lawn mower.com that 99% of the people buying and selling used to list their lawn mowers, one wouldn't be very smart not advertise there when selling or not to look there when buying.
The MLS is to get the word out you have a house for sale. Keeping track of the sales and how much they sold for and so on is just an added feature.
The MLS is one source appraisers use to gather data, other sources can be tax records, deed transfers, plats, loan officers, Realtor/Brokers, etc. Tax records can be accessed through the MLS, just an added feature; the MLS is a for profit company so the more they offer subscribers the more they can charge.