How would it not always work? If you start with $4000 and make a series of transactions and end up with $7200, all the individual gains and losses must add up to $3200, otherwise where'd the money come from?
You have assumed a fact not currently in evidence which is that the transaction involving the bitcoins, or at least what you are asserting involved whatever these undefined bitcoins are, is a capital gain. There are four main approaches which can have reasonable arguments made and the capital gain is just one of those approaches. You could also use a barter or foreign currency approach or even a super ninja approach which would result in no gain or tax liability (although this may be .... aggressive). Remember, the law is technical and all hinges on technicalities.
Well, if the transactions span across several years, and each individual transaction was under the tax threshold, then yes, I suppose you could reduce your tax liability, though you may have some explaining to do if the IRS notices a single large deposit to your bank account but you claimed it was from multiple transactions over several years. Good luck with that. (I'm not saying that won't work, but in my mind it's easier and safer to just write off the attention-grabbing deposit as a capital gain and be done with it rather than having to explain what Bitcoin is during an audit)
Have you ever been audited? First, it is a rare occurrence and second it really isn't that big of a deal so long as you have been taking a reasonable approach, founded in law with good record keeping. And if the IRS actually does audit you, given low percentage rates of this happening, then you (or better yet your tax attorney) and the agent may disagree on how a transaction should be treated and reasonable minds can differ on legal interpretation and in most cases the IRS will settle rather than litigate.
If you want to roll over, play dead and pay more taxes than you may be legally required to pay then that is your prerogative. And everyone has to do their own cost benefit analysis on their tax planning in running their business. But Congress has crafted tax law to provide incentives and disincentives for certain behavior and to not avail yourself of advantageous tax treatment would be a disregard for their intent in creating certain tax treatment to illicit certain behavior. While you are at it you can make a voluntary donation via a gift, with after tax money, to the US government
You can write a check payable to the Bureau of the Public Debt, and in the memo section, notate that it's a Gift to reduce the Debt Held by the Public. Mail your check to:
Attn Dept G
Bureau of the Public Debt
P. O. Box 2188
Parkersburg, WV 26106-2188
The question was specifically about paying capital gains tax on securities, which are not taxed until they are exchanged for cash. Many (indeed, most) other types of transactions are taxable whether they involve cash or not (eg, sales tax, income tax, etc) but that's not what the question was about.
"which are not taxed until they are exchanged for cash"
That is a blatant misstatement of the law. The issue is recognition
and recognition can happen in many different ways even if cash is not exchanged and in many cases will be calculated at fair market value.