Caesar's legion has the strongest currency in the wasteland, Vulpes could easily muster up 2000 caps to get in, the Frumentarii also have people in high places to get him a fake passport, the BOS has neither of these and I’m pretty sure the codex isn't too endorsing of selling off equipment or providing help to wastelanders.
Except the BoS has procurement specialists, Veronica is one of them, who are able to acquire resources and technology not available to the BoS. It'll also be much easier for them to steal and scavenge the resources after the war while the Legion and NCR are in retreat. The NCR and Legion can't take everything with them so there are going to be supply caches hidden all over the place. Fleeing NCR and Legion troops will be easy picking. Not to mention the fact that there's going to be equipment scattered all over the place from the battle. The Mojave is going to be filled with dead soldiers, as well as their guns and armor, and House's securitrons won't be able to clean up the mess until after they've made sure the area is secure. That gives BoS procurement specialists plenty of time to strip the best equipment off of dead soldiers.
For Benny it was easier to capture a securitron, House only had a handful of Mark 1 securitrons, in this situation he would have an army of mark 2 securitrons.
Funny how Benny managed to capture a securitron when House only had a handful of them and he didn't notice when one went missing from right under his nose.
House does have a lot more securitrons than before but again, this is after the war. Some securitrons had to have been either destroyed or damaged during the fighting. That gives the BoS survivors plenty of opportunities to gather securitron parts and capture damaged securitrons.
About the stealthboys, they were created by House's company; he would know how to combat them, also to do what you’re saying they would have to have a ridiculous amount of stealthboys and while the Mojave chapter may have had a large number of stealthboys, their base is buried in rubble. As for a power disruption, the Lucky 38 has its own reactor.
House clearly doesn't have very good defenses since the Courier can use them to sneak into his inner sanctum. As for the stealthboys that would be needed, how is that a big problem? The Nightkin have regularly used them for over 100 years. You really think the BoS survivors can't get enough to use for a whole day?
Also, sneaking in behind the Courier, the same courier who singlehandedly destroyed the rest of the BOS?
So? The Courier doesn't have X-Ray vision.
As for getting out alive, the BOS cannot just take control, you need the platinum chip to reset the administrator.
The chip is already in House's computer.
That doesn't mean House didn't detect him. House wants Caesar's Legion to continue to pose a threat enough to keep the NCR busy. Arcade Gannon even comments on Vulpes presence on the Strip, mentioning that either House knows about Vulpes or he does not, and how both options worry him. House himself will ask you not to harm Caesar when you go to the Fort.
Hell, if you kill House and tell him you did it for Yes Man, House's reply implies he knew about Yes Man all along.
And that shows he's fallible. He underestimated Inculta and Yes Man. Also, if he knew about Yes Man, why was he surprised about Benny's betrayal?