Let's start with the question of expectations on both sides. Unfortunately, restaurants don't usually post a notice saying "Average tip is 15% on the bill for food, excluding tax and alcoholic drinks, but including any dessert or special charge for sharing." So we're in a situation where we (as customers) don't know the expectations of the waiters. (I'll use the term "waiter" to mean either gender, and eschew the dreaded "waitperson.") There are four possibilities:
(1) If the waiter is expecting 15% on the total bill, and you leave 15% on the total bill, all is well.
(2) If the waiter is expecting 15% on the total bill and you leave 15% on the bill-less-tax, the waiter is disappointed. The conscientious waiter may worry what he/she did wrong. Or may think you're just a cheapskate. More on this later.
(3) If the waiter is expecting 15% on the bill-less-tax and you leave 15% on the bill-less-tax, all is well. However, see below.
(4) If the waiter is expecting 15% on the bill-less-tax and you leave 15% on the total bill, the waiter is pleased.
Since no clear expectations have been set, if there's going to be a possibility of miscommunication, in what direction would you want it to go? Personally I'd rather have the waiter pleased than disappointed, assuming the service was good, so I leave a tip based on the total bill. If I want the waiter to be disappointed--that is, if I want to deliver a message that service was crummy--then I'm going to leave a small tip or no tip. I'm not going to fart around with the small difference on the tax.
So, in the absence of instructions, I'd rather run the risk of slightly overtipping inadvertently rather than slightly undertipping.
A couple other things to bear in mind:
Most waiters don't have the time to figure out what the bill-less-tax is. It's often not even subtotaled on the check. Like your friend, most waiters are usually anticipating their earnings on the total bill.
If you've paid with a charge card, the restaurant pays a fee to the charge card company. Many restaurants (I was going to say "most", in my experience, but I haven't seen a formal survey) reduce the tip proportionately to reflect the costs to the credit card company. If you ask, they'll tell you it doesn't matter, but if you are friendly enough with a waiter to get the truth behind the polite fiction, often it DOES matter--the waiter is getting less than what you wrote on the charge slip.
But let's set all that aside. The bottom line is: The cost-less-tax thing is a bullshit argument so you can be a cheapskate. You're talking about an extra quarter or buck or whatever. It's a small difference for you. You're the patron at the restaurant, you can afford the price of the meal. The waiter or waitress works on a crummy salary and depends on tips to earn a living. So, big deal, you save a buck and the waiter feels hurt and undertipped and gets paid less. Sorry, bud, but that's about as cheap as it gets.
I will say that a relative-in-law of mine feels as you do. At first I thought it was an interesting concept, but then I saw that he was a cheapskate in everything else, too. I bet you still think 10% is a good tip and were shocked at my using 15% as "average." If so, get ready for this--the trend is to tip at still higher rates, with 18% or 20% becoming the norm.
If you really feel, as a matter of principle, that you shouldn't be tipping on the tax, then raise your tipping percentage. Instead of 15% on the bill-plus-tax, tip 16.3125% (Chicago has an 8.75% sales tax) on the bill-less-tax. If that's too much math (although you seem well equipped to deal with fine points), tip one-sixth of the bill-less-tax. Everyone will be happy.
The preceding applies strictly to the U.S. If you're dining outside the U.S., you need to look carefully at the menu. There's usually a statement that "service is included" or something similar, meaning that you needn't tip at all. The custom is usually to round up to the next whole amount as a tip, so if the bill were €23.45 (€ is the symbol for euros), you'd leave €24 or €25. That's a much more sensible system, if you ask me--to pay the waiters a reasonable salary and not have them depend on tips for their livelihood. A side benefit is that it's easier to divide a bill--everyone knows exactly what their share is, and there's no quibbling about what the tip share comes to.