> all the existing UTXO's that were already mined when the difficulty was high would also stay secure
Not really, because if there's not exactly one social consensus chain, then you can't prove you're the only owner of anything.
Not really, because if there's not exactly one social consensus chain, then you can't prove you're the only owner of anything.
Any UTXO that you create now, when the mining difficulty is quite high, is going to have a very high security, even if the mining difficulty goes down afterwards.
As the difficulty gets lower, the number of transactions to drop from the top gets higher, and maybe also less certain.
It makes no difference about the mining difficulty in the past. If double-spends are possible _today_ then you can't ever prove you own the coin, regardless of whether you could do it in the past.