Suppose a company could transfer an asset to an employee and have its value set as the employer's cost.

That's not how it works...The value would be the FMV at the time of the transfer to the employee. The cost basis would be the employer's cost. The income to the employee would be the net difference.

What would happen if any employer could do that with any employee and any asset?

They can't, because tax laws have addressed this situation for almost 100 years...

there is a separate carve out for "employee discounts", which is essentially the employer offering its employees its own products for something in the neighborhood of its own cost.

That carveout only applies to products being offered for the employee's own consumption unrelated to the needs of the business. Internal use of a company's own products for the needs of the business does not result in additional GAAP or tax deductions (meaning, if that product cost X to make/provide but they charge external customers Y, the only deduction is X, not Y).