While an employee could be an organization's most valuable asset, accountants record past transactions that can be measured.
Since an employee is not purchased, there is no past transaction and cost that the accountant can record in order to report this person as an asset owned by the entity. The salary and bonuses paid to a key employee are reported as expenses in the period in which the employee performed services.
Not being able to record a valuable employee as an asset is similar to a valuable brand name developed internally by a company over time. Since the brand name was not purchased from another entity, there is no past transaction and purchase cost to be recorded.
I assume that an entity's payment made to another professional sports team for a professional athlete's services for the next three years will result in recording the payment as an asset—a prepaid expense or deferred charge—that will then be amortized to expense over the three year contract.