The government literally already computes the number they expect you to owe. It's how they send you a letter if your own calculations come up short (or long, in which case they will in fact contact you to issue you a refund). If the government simply sends you their calculations (which they are already computing anyway) and you disagree, you would still be able to file an amended return with a company like TurboTax.
Why do you think it is—specifically—that a multitude of other governments can manage to accomplish this feat, but the United States government shouldn't be able to?