I'm not sure of the situation in the US, but I do know the UK one. Bear in mind I'm talking about the UK so some specifics may vary.
First, be aware that sites like "Just Giving" charge a 5% fee (plus a few fixed costs) and have a much much wider reach than you could. So you might find that places are unwilling to work with a (no offence) untried and untested organisation such as yourself when they'd be "paying" exactly the same cut to a multinational brand with massive name recognition.
$10,000 profit is also a colossal amount of profit to make, I think you might be setting your sights very high there. I'm not sure if that was a number plucked from the air or an actual figure you a thinking of but, if the latter, I'd suggest its too high. If making $10,000 profit were easy, everyone would do it.
There is, over here, a type of legal entity called a "Social Enterprise" - it basically sits between a charity and a business. I'm sure there'll be a US equivalent but I don't know what it is. That's what you're talking about setting up. Your fee - which I see nothing ethically against - is earned income and would need to be taxed as such, meaning you need a legal structure to do that.
You don't need the charity's permission to donate to them, but you do need their permission to use their name. You can throw a fundraising event for "Charity" and then give out the profits as you see fit, but if you want to throw one for "Specific Charity" then, as BeMi says, you need their permission.
I suspect most will be unwilling to work with someone who rotates - I know we won't. The issue is that your events get name recognition which cuts in to us: Lets say I want to donate to Charity X. I attend your fundraiser and make my donation. Next paycheck I want to donate again and so I attend another of your fundraisers - but now my money goes to Charity Y. Sure, you can say "We'll make it clear who the money goes to" and all of that but people don't read things properly and so we, and as I say I suspect most places, don't work with organisations like that.
Errrrr....what else? Be aware that people will complain about your cut. Taking one is standard, your proposed one isn't outrageously high but people will complain. I promise.
I don't mean to pooh-pooh the idea, but as it stands I'm not sure how feasible it is. What might be easier is starting your own charity which distributes funds; that would avoid some of your problems and even more if you kept that distribution standard - 25% goes to Charity X, 25% to Charity Y, etc.