"I'm trying to understand what the advantage of having a car allowance would be vs enhanced compensation."

As Bill pointed out, it's just semantics. Same concept, functionally.

"If mileage is not tracked, the car allowance is compensation."

Because it's just Money. You are relating things that don't relate. If mileage is Tracked and reported and meets An accountable Plan requirements, the employer can pay out that amount under the terms of An Accountable Plan. If I don't need to account for it, and my employer gives my money anyway, it's Taxable. It's Money, not Money for a qualifying reason that is proven.

"Is that difference that if mileage is tracked for car allowance it is not taxable? Using the car allowance gives you both options?"

There is no such thing as Not Taxable "allowance." They are not "tracking mileage" so much as "tracking business." If you think of it like that, it helps. The same would be true for Food and Paper. If I bring you a receipt for printer paper, my lunch, and I hand you that printer paper, you reimburse me for the Office Supplies. I bought from Staples and you bought from me. My lunch is not reimbursed. We all have to eat. It was my choice to eat out, not pack a lunch or go home for lunch.

You might be confusing Mileage Allowance (for purposes of the IRS) with Actual Costs. You cannot pay Actual Costs for a car not owned by the business. You cannot pay to repair the employee's transmission, have it towed, or all new tires. The Employee owns the car. If the employer wants to pay for those, that's Bonus, as taxable wage. It's more money, in other words.

Or, you might be thinking of Per Diem, which is not really an Allowance. It's a way to Reduce Paperwork. The IRS sets per diem so that we don't need to turn in receipts for business lodging and meals that qualify as business purpose, like out of town trips over a few nights gone.