But it's already different. NPCs and adversaries don't usually get adventurers equipment last I checked. They also have fairly generic stats unless otherwise noted.
Again, no. Worse equipment and lower stats are handcaps within the same rule set that adventurers operate in. Giving adventurers exclusive bonuses outside of all stats, equipment, etc etc, breaks the rules into two - "haves" and "have nots", or "adventurers" and "everybody else", as you will.
There's a very big design difference between tweaking numbers (gold amount in gear, stat totals) and inventing new rules that can only apply to a subset. It's like the difference between a cheating AI in a game and an AI that gets advantages within the rules. Almost every strategy game AI gets advantages within the rules, for example; bonus resources, faster build times, and so on. Compare that to the old game Empire Earth, where the AI did not need any resources to construct buildings or units, automatically received technology advances without having to spend any money or time researching them, did not have to spend any time or units to scout the map, etc.
That's the difference between adventurers being richer and having better stats, versus them having exclusive, adventurer-only bonuses that a simple commoner can never, under any circumstances, have.
Unless I am mistaken, most opponents with class levels do have *adventurer* class levels, meaning they would get the same bonuses as the player characters.
Which, effectively, would make them better than they were before, because they normally don´t have the money to buy all the stat enhancers which player characters can buy.
I certainly don´t bother to let the players in my campaign fight commoners, warriors and aristocrats. Do you? Because if not, your argument that suddenly there is that huge gap between PCs and NPCs is spurious at best.