I quite often get accused of pedantry, but the objection to your formulation is 'while the shutter was open' doesn't strictly apply to electronic shutters. But then, neither does the word 'shutter'. That's XPat's objection. Porky's objection is because he hasn't enough basic understanding to realise that your definition is equivalent to E = I × t. The advantage of your formulation is that whilst strictly not completely correct since mechanical shutters ceased to be the only option, the variance does not cause any conceptual issues, and it's more accessible to lay people than 'integration time'.
That is exactly my point. I posted either in this or another thread that I have not yet come across a beginner who has not been able to understand that the definition applies to all cameras once they understand the similarities in concept between mechanical and electronic shutters.
The definition I use is a layman's version of H = E x t.
exposure - amount of light that struck the sensor per unit area while the shutter was open
Agree. Objecting to this usage is akin to objecting to using the phrase "dialing the number on your phone" or "hanging up after the conversation is over". Or objecting to use of the word "throttle" in a modern, fuel-injected vehicle.
Integration time is a bit difficult to explain if we are trying to make a definition of exposure work for film. But also in some cases with film there is no shutter at all, only a lens cap ;)
It does, absolutely. But, technically, it isn't a shutter. And the funny thing here, on top of that, the motion with the cap isn't meant to ensure the same exposure across the frame. My personal preference is something along of "while the light hits the sensitive area".