Your Q: Won’t the initial “deposit” of 10k USDC from borrowing be seen by Koinly as 10k USDC in income without any basis?
Answer (based in part on Koinly Help article): No. Deposit txns that are not tagged or labelled will not be treated by Koinly as taxable transactions. Rather, the borrowed crypto (a deposit) will be assigned a cost base equal to its market value on the loan date. A capital gain or loss will be incurred when the borrowed crypto is disposed of, whether by spending it, selling it or repaying the loan.
Note that the Koinly Help article is based on a tax position that borrowing crypto is a property acquisition (akin to acquiring shares or real estate) rather than a loan tx (aking to borrowing fiat from the bank). A sale or disosal of acquired property gives rise to a capital gain or capital loss in most jurisdictions.
However, you need to look at the specific tax treatment of crypto borrowings in your jurisdiction to see whether the jurisdiction treats the particular borrowing structure as a loan for tax purposes or as an acquisition of property. The Koinly Help article is based on the latter approach as this is the position that is best supported by tax laws in most jurisdictions.
Here is commentary on the likely position in the US where the IRS has not provided specific guidance (AFAIK). "The major difficulty in treating crypto loans as loans for tax purposes is IRS Notice 2014-21, which states that (at least as far as the IRS is concerned) convertible virtual currency is property (Notice 2014-21, Q&A-2), and according to established case law, a loan for tax purposes is a “a debt [that] necessarily involves an obligation to pay money and not an obligation to deliver property” (R.S. Stahl v. United States , 441 F. 2d 999 (1970)).
Hope this helps.