My first playthrough, I sided with House. I figured that I owed him, since he saved my life. But he asks you to do some pretty dastardly things to repay that debt...like wiping out the BOS. My character knew nothing about the BOS, so it was pretty much a mission to slaughter a bunch of people hiding underground. The courier's responsibilty is to give House the chip, since it is his...but then he orders you to do what it takes to ensure his that he has all of the power. That's why he saved the courier's life...so he could get his chip (justified) and have a slave to do his bidding (unjustified). No freedom of choice.
Are the NCR and the Legion so different? if you can't get the minor factions in line your to eliminate them. Caesar and Col. Moore feel just as bossy as Mr. House [Its the lower ranking NCR who are happy to see you if your rep is good]. The NCR want to kill House because they want to annex the whole region. House is only opposed to the NCR because they want to take over all of Vegas. If they'd keep to the treaty so would House. But the NCR won't they send you to assassinate him because he's a threat to there power.
And what about his grand plan? Spaceships and cities on the moon and what not. Sounds great, but one thing casts doubt on all of that, that perhaps his calculations might be wrong: Benny. Of all the people on the Strip, hell out of all the people in the Mojave, Mr House picked a back-stabbing two-timing weasel as his agent and assumed that agent would be loyal to him to the end. Trusting Benny as his agent was a massive miscalculation on his part. Mr House didn't just pick Benny's name out of a hat. He anolyzed all of his available data and decided that this back-stabbing two timing weasel was the best person to help him. It shows that technology aside, no Mr House is not omniscient and that his predictions for the future are not mathematical certainties.
Your assuming Benny showed backstabbing weasel characteristics before he betrayed House. And his predictions may not be certainties but he gets real damn close. He saw the Great War coming and properly prepared New Vegas to survive, had the war happened but a day later. Well we wouldn't have a game would we. He can predict how The Legion and the NCR respond to things,.
The only two people in the entire Mojave he can't predict is Benny and the Courier. But even with Benny he had Victor dig you out minutes after you were shot. Once again the difference of an hour was critical if Victor got there sooner he'd probably have filled Benny with lead. Unless House knew you'd survive and become the unstoppable machine capable of tipping the balance but thats just scary accurate.
His predictions may not be certain, but he's damn close. Close enough to give him a shot. Mr. House has to trust the Courier because he has no choice, the battle for hoover dam is drawing near and he calculates you have the capability. If he had a member of the legion in his pocket he'd have used him to get the chip and activate his army.
And of course Mr. House's calculations are only wrong if you don't side with him. If the Courier wants to make the world a better place, House has a plan to do it and it doesn't involve conquering everyone in sight. If the Courier just wants luxury and power. House provides that as thanks for his hardwork.
Sure YOU COULD rule Vegas yourself with Yes Man but who wants all that paperwork, either retire to the Lucky 38 and let House run things or continue to be his right hand and go where the action is.
The Mr. House ending differs based on karma and shows that the Courier maintains influence on policy even with House in charge.