You are excluding one very important point from your cost-benefit analysis, and another secondary follow-on benefit.
The first: Time. Presently, if it is decided that a target absolutely, positively has to be blown up tonight, then somebody has to get on the horn to Whiteman (or Guam) and get the ground crews to work. That’s a couple of hours. Get the crews out and strapped in, platforms rotated up and out, and settle in to fly for 12-18 hours to target. Oh, and, better hope it’s dark over target for your mission profile...
With our orbiting garbage can full of rods, the ordnance is already there. Depending on the amount of cans in orbit, you could annihilate your target before the first bomber ground crewman gets to work.
While it is indeed true that the Stealth platforms have learned the secret Ninja art of not being seen, they still have the logistical trail of any other conventional platform.
Secondly, that kind of launch schedule gets a lot of boosters flying. This tends to (unless you’re working with NASA) drive the cost of such launches down. Additionally, you are learning about your launchers, equipment and figuring out how to make them better. With cheaper and better access to LEO, a lot of avenues open up.
As to use, the mere existence of such an operational system would cause a mass outbreak of rationality. Weapons do not necessarily have to be used to be effective...
Time is exactly their weakness.
It gives the recipient only a short time to decide that they had better retaliate with nuclear weapons, because no one will believe your weapon has only a conventional warhead. About as worthy an idea as the much-ridiculed conventional ICBM....
And yes, they will detect it.
I guess the real question about the LEO weapon would be about whether the U.S. will continue to hold the high ground in space. So far these days, it sure doesn’t sound like it.
I’d rather have a bomber on their coastline shooting an ALCM that flies stealthily at about 100 feet AGL.