After peaking at approx $800 bil in Dec 2017, cryptocurrency market cap gradually decreased (~ 289 bil on 23 Jul 2018). But in contrast, the number of exchanges
increased dramatically during that time.
Do people want to grab a piece of a smaller cake or they believe the cake become bigger? I am so doubtful about the latter scenario.
Your whole thinking is off. Why shouldn't the number of exchanges increase just because the market crash? Would they still not collect fees from people trading and make money? What smaller cake, the market is still larger than it was a year and a half ago, probably a year ago. Grab a piece of the smaller pie. That's like saying why would anyone want to buy the dip, why not wait until it's at an ATH to get in.