"I can't think of a reason they would need HBO or FOX to make things happen."
I can think of three: cost, distribution and risk.
The cost to produce the show likely isn't cheap - could be as high as $1m an episode, and the risk is you have a bomb after you've invested in, say 5-8 episodes. You could get investors to put in money - but who knows if Mike Judge is interested in that - he might just want to make a great show.
Or you just partner with HBO and get to make the show on a large budget with high end production values, along with HBO's very strong promotional arm to push it - and you still get a boatload of money plus residuals.
Louis CK can do what he does because he's selling a live show - the costs are predicable and one-time (or maybe a few times if he records multiple shows). Not that there isn't some risk - but Louis CK can also offset the cost side by what he gets on ticket sales - so he's probably even on the cost side before he even tries to sell it on the internet.
TL;DR: You can't compare filming a show with filming a series.