Your idea roughly goes into the direction of what the industry has started implementing: Tunable Replica Circuits:

https://www.intel.com/content/www/us/en/newsroom/news/the-st...

This mitigation helps until the attackers stop confining themselves to the supply pins. You can do voltage fault injection through any exposed metal (or metal that can be made exposed), and the attacker can be entirely happy with attacks where they don't actually pull the voltage plane down, but instead just make some specific circuit a bit iffy by injecting an opposite voltage at some specific point and with low enough current that it's undetectable when looking at the chip as whole.

Approaches such as yours do make the attack require a lot more skill to accomplish.

If you spike the voltage on other pin you'd most likely trigger ESD protection which is just a diode that's connected to one of the power rails, and spike the chip's power supply.

Which would be detected if internal watchdog monitors voltages. But if spikes are short enough they might be pretty hard (or just expensive) to detect.