This isn't even the main problem. Im not sure if you should declare it as income tax or as you say, 0 cost basis investment, of course you will always pay some tax in any case, the main problem is if you did not keep track record to prove where your bitcoins come from, they could simply claim that the origin could be from drug dealing or some criminal activity, note the "could". You can't prove it, they can't prove it, there is a conflict there. This situation varies a lot depending jurisdiction. Is this grey area that scares me the most. Worst case scenario and you will lose your coins as they confiscate them due "Illegal assets" or something.
For instance, many exchanges are now dead and people have lost tons of track records, or even current exchanges have extremely poor policies in trackrecord keeping, for instance Livecoin is an absolute mess which keeps only the last 30 days of trades, so I have lost some trading records there... honestly it is a nightmare trying to keep track of everything. Now if you try to sell some of these coins involved in lost records you may have problems. Like I said, a total nightmare.
Then keep records. The bitcoin blockchain is one entire public ledger so it's not difficult to find your transactions nor will it be for the tax authorities. Besides, if there's no link from the money going to you then there's obviously no link that the money came from crime either and they can't prosecute you based on nothing or mere suspicions. The Tax authorities likely won't be as lazy or as stupid as those who are claiming they've kept no records so they'll be tracing those funds if they want to prosecute and they'll either find that you've earned them legitimately or that you've been doing something criminal. If anyone is worried about being painted as as a digital drug dealer then keep records. It's not hard to keep a spreadsheet updated every time you receive a bitcoin payment and this is something you should be doing anyway for your own records.