I assume you are going to up the ranged weapons damage as well, then?
That's the reason there is aggravated damage. And characters with 10 soak dice are not the norm. Only heavily combat-oriented (and very powerful) characters have that sort of stats. Not only that, but it also introduces a huge imbalance between going bare-fisted and carrying a knife or a sword, to the point of rendering the brawl skill useless, unless you have Protean.
It's interesting that you bring up the Assamites, considering that their special brand Discipline allows them to deal aggravated damage with melee weapons. I'd rather not be hit with 10+ dice of aggravated damage several times in a round from a regular melee weapon if I can help it. In fact, I'd probably be playing an Assamite if I had known we were using this kind of crazy damage. "
Well, you are the GM and you have the final say on any rules matter. But in my experience, modifying the rules this way can result in unpleasant imbalances, as a lucky roll can end the "Final Boss" in the first stroke of a fight, somewhat ruining the Chronicle, or result in Final Death for a PC "before they know what hit them".
But hey, you're the boss.