The bank that owns the loan would record a corresponding $100k asset.

You're not getting my point. Education itself is a form of wealth in terms of increased future earnings; otherwise few would pay for it. That wealth doesn't show up on anybody's balance sheet because it's hard to measure, but it still there. When some millennial says they have negative net worth due to student loans, they're not accounting for the positive value that their education affords them due to the fact they can do skilled labor.

Look at it this way -- if a company A has an EBITDA of $20k/year and company B has an EBITDA of $40k/year, the MBAs will have no problem assigning values to these companies. And companies can increase their earnings by going into debt such that their net worth as measured by these calculations can increase. But substitute a human in, and suddenly everybody has negative net worth.

This is incorrect. The principal is a liability to the issuer. Income from loan payments are subtracted from the balance as they come in.

The cash from the loan is an asset for the borrower, until it is presumptively paid to a third party.

Prior to this transaction the bank owned $100k in cash, also valued as a $100k asset. There's no corresponding increase in wealth for the lender.