Crypto supply will always be higher than the demand because they are usually millions or more than that. Price change can also be termed as volatility. The volatility is higher when more people are selling apart from buying a coin. Price can go low if there are less demand and it happens due to several reasons like people are in crises but if not, maybe the exchange or the coin have only gone bad.
OP is talking about rates, and by that I think the services fee of an exchange is also covered with it. This is the same to what you said about how an exchange operates, this is why it is important to analyse them if which exchange will suit us according to our needs.
I do agree that volatility is important for an exchange because it means there are a lot of people trading in that situation and if people are trading then they are doing a good job. I know that trading fee is the way to make money for these places, so when there is volatility that means they make the most money.
If we are talking about just the fee, then the fee depends on the power of the exchange that can ask it, one that asks higher means that they know you won't leave with higher, and the one asking lower means they are trying to get you to use them. The prices however are a different topic, these days I do not think that there are many places with different prices, I do not believe that many like that stayed until this day.