Capital gains are taxable when they are realized unless statutory exceptions apply, under the U.S. Internal Revenue Code.
A loan is not considered income. When a creditor sells collateral in order to secure payment of a debt, the sale by the creditor of collateral owned by the debtor is a realization event that triggers capital gains taxation on the part of the debtor.
This doesn't mean that loan provided no tax benefit.
Suppose that the loan defaulted two days after the owner of the collateral died. Due to the step up in basis of capital gains at death, under Internal Revenue Code § 1014, the collateral would not be treated as if it was purchased at its negligible actual purchase price, instead it would be treated as if it was purchased at fair market value on date of death, effectively forgiving all capital gains taxes on the accrued by unrealized capital gains from date of purchase to date of death. (FYI, Canada taxes unrealized capital gains at death, unlike the U.S.)
Similarly, suppose that the investment was investment real estate, rather than bitcoin, and the loan was an unsecured line of credit, rather than a loan secured by collateral. The investor-debtor could sell the investment real estate and reinvest the proceeds in different real estate using someone called a "qualified intermediary" to hold the proceeds between transactions and complying with certain tax regulations, to avoid triggering the realization and taxation of the capital gains in the original real estate, using Section 1031 of the Internal Revenue Code.
Also, the loan, even if eventually called or paid off with liquidated bitcoin by the debtor (rather than having it seized by the creditor), still made it possible to defer taxation of the capital gain. All other things being equal, deferral of taxation is an economic benefit. It means that you are investing before tax dollars, rather than a smaller amount of after tax dollars, and thus earning greater returns if the investment is increasing in value.
And, if the tax rate that the capital gains are subject to is lower when the investment is sold than when the loan was taken out, that is an additional benefit. But it is also possible that the tax rate that the capital gains are subject to will be higher when the investment is sold than when the loan was taken out, and that could outweigh any economic benefits that come from tax deferral.
In particular, sometimes the capital gains tax rate depends upon the holding period of the asset. Suppose you have owned the asset for eleven months, but there is a lower rate available with a two year holding period (or a one year holding period). If you borrow the funds you need to spend for fourteen months, then sell the investment and use the proceeds to pay off the loan, you have not only deferred taxation, you have also secured a lower long term capital gains tax rate rather than a higher short term capital gains tax rate.
There are some anti-evasion rules designed to limit these kinds of transactions, such as the "wash sale rule" that limits attempts to realize losses by briefly selling assets and then repurchasing them, and rules to prevent people from avoiding tax by transferring assets by gift to a terminally ill person (which doesn't result in the realization of capital gain and instead gives the asset a "carryover basis") who then leaves it to the person who gave it to him in his will. So, merely following the logic of the basis rules about taxation of loans and capital gains doesn't always work. There are maybe half a dozen or a dozen of these rules that each apply in very specific circumstances and are too varied to recite in this answer.
The other consideration is that simultaneously having an investment asset whose value changes over time, and a loan, is riskier than then selling the asset and spending the proceeds. In the example in the OP, the creditor would seize the $100K in payment of the debt, and the debtor would owe $33K in taxes (which are harder than the loan itself to discharge in bankruptcy) that would have to be paid from other assets of the debtor.
