1) Why do we even have a rep cap in the first place? Doesn't it deprive users of their hard-earned rep?
The rep cap is perhaps more important on larger sites, where questions and answers receive many more views and votes. On Chemistry, we have on average less traffic and less of a need for this.
However, the effect of the recent Hot Network Question (HNQ): Why doesn't water burn? may be used as an example. The current accepted answer has 149 upvotes, corresponding to a total of 1490 reputation. That alone would propel the user 3/4 of the way to making edits without having to pass through the queue. For a user whose participation on the site consists of a suggested edit, several comments, and one answer, this was obviously seen as too fast a rep gain. It can get even worse on other sites.
The idea is therefore to force users to be around for a while before they start getting site privileges. This is a step that is necessary on Stack Exchange, a website which adopts a community moderation model. If all power was solely vested in the diamond moderators, then there would be no need for a rep cap, as users would have no use for reputation.
As for whether reputation is "hard-earned" is very debatable. The answer to that question, while good, clearly has less content compared to some others that the site sees. The fact is that upvotes to questions and answers are mostly random. Many users here will tell you that the contributions that they are most proud of did not garner many upvotes, and many of their most highly upvoted contributions are not particularly well-written either. Personally, I have a tendency to type detailed, MathJax-heavy answers. As of the time of writing, this answer on the quantum mechanics of coupled spins gets 2 upvotes, whereas this quickfire answer gets 14. Does my short answer "deserve" seven times more upvotes than the other one?
Finally, imaginary internet points should really not be the aim of participation on the site. Participation should, ideally, solely be based on the desire to contribute information or learn. Gaining reputation is simply a side effect of doing that well. Therefore, I do not think that anybody should be affronted that they receive less reputation than they "deserve".
2) What happens to the rep you receive past the rep cap? Does it simply vanish (like my 70 rep)? Can you 'redeem' it somehow, at a later time? Or is there some kind of trade-off involved here?
Yes, it is gone forever, and no, it cannot be redeemed.