One reason is because if AS was not a factor in this particular battle you would never have initiative to play a card like SH that would interrupt the protect ability.
I don't believe that is what jmhartz is implying. I think he is assuming that SH could be played legally, but still not interrupt the protect.
Correct. In order for an "Interrupt the battle" ability to interrupt a Protect ability, the card with the Protect ability must be in battle. SH can target Uzzah in discard when Uzzah was the last card played in battle, because that's one of the things "Interrupt the Battle" can interrupt. But if Uzzah is not the last card played in battle and is in a discard pile, SH can't interrupt Uzzah's protection because Uzzah is not in battle.
This hearkens back to the "Can Daniel negate Gates of Hell?" conversation from a few years back. The conversation started when an elder stated that if you could band Habakkuk into battle after Uzzah had discarded himself, Habakkuk would negate Uzzah's protection. The conclusion ended up being no, Habakkuk wouldn't negate Uzzah because Uzzah was not in play.