It's perfectly fine and good for Peter to inspire others to be heroes, but do they have to take his identity/image/likeness/symbol to do it? Is it so hard to create your own unique identity and be your own person, do you need to copy/steal another's identity. Not every hero identity needs to be seen as a mantle to be appropriated or handed down. It just highlights a laziness in comics where instead of creating unique heroes with their own identity they just leech off an existing popular hero to boost the new one, often to mixed or negative results. And finally not every hero needs to have a "family", the batfamily is one thing, though that has gotten out of hand; but was a spider family a thing that was needed. At any rate its a moot point, what's done is done. The best one can hope for is that Peter is not screwed over or thrown under the bus for the benefit of others like Batman regularly is.