Sorry to drag this on, but I do believe in putting an end to
cargo-cult advice.
I have verified with my SC that the brake pedal "hard reset" is misinformation. There is an actual hard reset (not the factory reset), but the procedure is way more complicated than an additional brake hold and can't be done by the owner. The origin of the brake application advice was likely for safety considerations. Of course we all know you CAN reset your UI while driving, which Tesla strongly discourages for obvious reasons.
The "hold until emblem appears" is official advice (it's in the manual). But it's not a requirement. It's akin to waiting 30 seconds when powercycling a cable modem. Essentially, tell the customer to do it longer than required so they don't accidentally stop too early.
Also, if there were a "hard reset" procedure that was more likely to resolve problems, wouldn't that procedure be specified in the manual, particularly if it's just the application of the brake? Why would you ever soft reset vs hard? Esp when they both appear to take the same amount of time?