You can prove the origin of your coins, though. Let's say you have some signature campaign earnings as the OP indicates. Those transactions and the threads that describe them are archived. You can sign an message from your receiving address. Mintpal's wallets are (or can be) identified. You can show the transaction from your campaign receiving address to Mintpal, and you can show a withdrawal from Mintpal (on the blockchain) to an address you control.

Segwit's scripting complicates this, but this wasn't an issue in the days of Mintpal.

Similarly, if you wired money to an exchange to buy BTC, you can show bank records that reflect that. And you can show withdrawals on the blockchain that reflect your BTC holdings from that transaction.

As with other IRS investigations, they would need to prove that you received income that went unreported. The only way that your trading records can be disproven is by direct coordination with an exchange. If an exchange did not enforce KYC, this becomes difficult. I think that blockchain records reflecting the coins under your control during the relevant times are more than enough to show good faith effort. I think this is especially true in the case of exchanges that disappeared.