It absolutely would have been faster. The depot (where it gets mailed to) gets priority for parts, meaning its very rare for a part constraint to affect them, whereas Apple retail stores and AASPs are at the mercy of in house inventory, available replacement inventory, and shipping times. If Apple says they don't have a part in stock and offers the option to send it to the depot, take it unless you're scared about data loss.
Thats like saying I should have expected BMW to replace my M3 when the ECU failed and took a few days to arrive, you know, because it was the top of the line for that model range. Sorry, it doesn't make sense on many, many, levels. When you get to a low enough price point (at least at the consumer's eyes) it makes sense, hence why it's so common with iOS devices. But not multi-component larger devices that cost thousands of dollars. You're paying for a great computer, not for top tier replacement when the smallest failure occurs.