Anyway, Makomk, thanks for your insights. One followup question re: what happens if mining pools start ditching the oldest parts of the blockchain:
If I take a wallet out of storage from time to time and send its entire amount of BTC to a new wallet, am I correct in assuming these coins are essentially re-minted as "new" coins that appear later in the blockchain, circumventing this potential problem?
Your questions seem to come from a misunderstanding of the way this all works. Don't feel bad, it is a big system and hard to get your head around.
There are no coins.
A transaction redeems one or more previous transactions, and has one or more outputs. Redeemed transactions are redeemed as a whole, never in parts. If the redeemed transactions have more value than the combined value of the outputs, the difference is a mining fee.
There is a safe way to discard old transactions, and that is to delete transactions that were redeemed more than X blocks in the past, where X is large enough that you feel confident that the chain can't be reverted that deeply. Recent reports suggest that around 75% of old transactions could be pruned in this way.
If that isn't good enough, and some miners want to discard old transactions that haven't been redeemed yet, those miners will see transactions that attempt to redeem them as invalid and won't include them in new blocks. This practice is unlikely to become dominant though, because they will be missing out on potential fees when those transactions are eventually redeemed, so other miners will have even more inventive to keep them. Actually, I doubt that even a single miner will ever do unsafe pruning for that reason.
And yes, if you send your balance to a new wallet, the new wallet will have a newly created and verified transaction. In that sense, the "coins" will be new. In the other sense, either the coins still don't exist, or they are just as old as before.