If you have an electronics store nearby with resources like diodes, resistors, capacitors then you might not want to bother. For practicing your soldering iron skills then it's perfect. Go ahead and remove as many components as you can from that power supply (the bigger caps should have their pins shorted together before attempting to de-solder (just in case ). The big coils in your box rarely ever go bad, so you don't need to hold on to a lot of those. Transistors might be re-usable at times for pins , ICs would be really doubtful coming from power supplies. I suggest to only keeps parts that you can easily identify by looking at their part number on google and finding their datasheet. Transistors , diodes used to have easy to read markings to identify them. Nowadays there is less and less info on parts you see in appliances, and that's very true for power supplies. A lot of ICs are obscure asian parts that you won't find any info on. Also a power supply handles power, so it doesn't use logic gates or control ICs or transistors that would typically be used in pinballs, especially older ones. This means that components from a power supply would most often be found, in a power supply (transistors and ICs). I don't go through scrap boards to remove parts and make an inventory for repairs. Over time you end up buying more and more little parts, or extras when you fix something and end up with a stash of new parts. You keep those old boards stashed somewhere for a random resistance you don't find in your inventory, an old connector, transistor, etc.
But for pratice, and parts that *might* be needed on pinballs would be resistors , diodes, transistors, connectors, capacitors, could all have a use once in a while. Usually those parts cost a few cents each when they are readily available to you.