These are interesting questions indeed.
Well, you can’t ask for double because I would just use the next larger denomination instead 
How would one go about collecting all the coins of a given denomination? It would take a lot of time even if it’s possible. Let’s not forget they should also collect the coins from at least a few denominations below the targeted one, or else people would use those instead, and then one or two denominations above, or else people would just accept the slightly larger rounding error than before.
Also, driving up the price of one denomination is likely to ripple through the whole thing (it would have the time, as this is not something that can be done overnight), which would render the operation meaningless.
We would have a little more finer grained set of denominations with a much smoother distribution of coins. We would also have wallets that would spend your coins carefully, making sure you had a variety of coins if you need them later.