It seems like I must've worded it wrong, because everyone has misunderstood it so far
Original TwlBg, no matter what you do, will always write to the WiFi flash on boot. Period. Anything you do, this write always happens, and it's not optional on an unpatched TwlBg. Holding or not holding START/SELECT has no effect either, because touch screen callibration data is also always written to the WiFi flash, no matter what. This wears out the WiFi flash unnecessarily, because it's not smart enough to filter out re-writes with the same data. If you wear out the WiFi flash enough so that the settings don't stay as you have written them, it'll permabrick* DS(i) mode.
This anti-wear patch remedies this by letting the user decide whether something doesn't work as they expect, and reboot into DS mode while holding X to fix the issues caused by not updating the WiFi flash.
Basically all the anti-wear patch does is make the WiFi flash writing optional. If you're not holding X on boot, it will not write to the WiFi flash, which is good, because this preserves its life, considering that more than 99.99% of the times the same data would've been rewritten there over and over again.
When you're in the less than 0.01% category (has recallibrated touchscreen, has changed system time, or using START/SELECT on a game which looks bad upscaled), you can just force a WiFi flash write by holding X at boot, correcting time and touchscreen callibration issues.
* A permabrick happens because the DS firmware or DS games can't read it properly, resulting in a permanent softlock. However, this is only a permabrick on 3DSes where WiFi is soldered onto the motherboard, although replacing the WiFi card is still a not-so-good idea. This also only affects DS(i) mode, because GBA mode completely bypasses DS mode, and homebrew replacements (like open_agb_firm) don't have this issue.