That's what I would have done. Also, it would have given Raimi more time to make Brock a more interesting character, and thus a more interesting villain. So many people b*tch and moan about how Venom is "too one dimensional" and such. Well, if you don't like it, change it! Raimi could have used this opportunity to make Brock a better villain but instead he was thrown in as more an afterthought.
Personally, I would have made Brock a bit of a mentor figure to Peter. Someone that Pete tags along with on journalism assignments and such. I would have had Brock be an alright guy, but someone who also could be a major jerk. I'd make him a typical imperfect person, someone who wants to the do the right thing but more often then not does the wrong thing.
I would have changed out the Sandman family storyline and replaced it with Brock. Have Brock be the one with the sick daughter, except he's trying to take care of her on his own. His wife left, and a good deal of blame lies with Eddy, because he wasn't the ideal spouse.
Eddy needs money to get his daughter medical treatment, but he also has a gambling problem and owes money to some bad people. So when he's desperate, he rips off Peter's pics to pay the debts off. Then, when Pete gets the black costume he exposes Brock (much like in the movie) but doesn't realize that by getting Brock fired he's also pretty much screwed the guy and his daughter because now Brock can't pay off the gambling debts fully.
The guys who Brock owes money come to his house and kill his daughter to teach him a "lesson" and Brock, overtaken by grief goes to commit suicide at a church, and you know what happens from there.
The sad thing is, I just thought that up, and I think it makes Brock more interesting as a character, and it would give him a better motive as a villain, because not only did Peter ruin his life, he inadvertently ended Brock's daughter's.