It's mostly that they're cheap parts, so they sound and/or play cheaply.
My experience is that cheap things can perform absolutely fine, and expensive things can perform poorly. That's not to say that sometimes being able to spend a little extra can't be useful, as it gives you a wider choice - but don't fall into the trap of thinking that more expensive is necessarily better. Cheap instruments can play very well and sound very good. Expensive instruments can have dreadful flaws. The same goes for parts.
'Cheap' isn't in itself a problem. Rather it's a good thing - it means you have more money left for times when the more expensive choice actually is more suitable for you (for some specific reason other than it being expensive!)
I'm wondering if I should also upgrade other parts such as the volume/tone control pots, the 5-way switch, and the input jack.
My experience is that (assuming you use the same value and taper pots), these things will make very little difference. But it sounds like you're enjoying deconstructing your guitar as a learning experience anyway. Why not try and find out?
One thing you will gain from this process is an excellent understanding of how the instrument works, which is very useful.