Re: How long will they stay up?
Take a deep breath, grab a cup of tea and sit down to go through numbers. Yes, it is boring, but sometimes very instructive.
OK. Where are these numbers? I'm presuming you've done them - as your post concludes that the thing isn't workable?
Had a quick look at the wiki article on this, which appears to have had a lot of input by SpaceX. They're talking satellites of 100-500kg. Small enough to piggyback a couple on other launches. Even if we assume nearer the top 500kg weight, that means a Falcon 9 might lift 50-odd. Falcon Heavy being able to do 3 times that.
BFR being able to lift 6 times that at 150 tonnes to LEO. And be re-usable of course.
OK we have to also factor physical size into this. And how you deploy the damned things in multiples of 10. It also matters what size the constellation has to be to become viable. If you need 5,000 up before you can sell to the first customer, then you're in trouble. But if you can deploy say 500 and go operational then you can test the system and start getting revenue. So long as you don't sign up more customers than you have bandwidth. Say you could get 400 up in 5 launches that you pay for (on re-used rockets that are therefore essentially free), and another 100 piggybacking on the 20-30 launches a year SpaceX do for paying customers. Those 4 launches are going to cost you money, but we're talking a few millions to SpaceX - rather than half a billion to a customer - though there's the opportunity cost of what they could sell those rockets for...
Now let's look at revenue. 10m US customers, paying $600 per year ($50 a month) = $6 billion per year. And as they're not in geosynchronous orbit, they get global coverage out of this network, so can make money elsewhere.
Your infrastructure costs are incredibly cheap. Because you don't have vast numbers of engineers and a huge network and property to maintain. You just build loads of disposable-ish satellites - and they can be relatively cheap because you're mass producing them and they don't need to be engineered to last stupidly long.
Is this viable? I've no idea. I'd have thought that 500 medium sized satellites would be better than 12,000 smaller ones. There's going to be global objections to launching a constellation that huge, covering that much of the sky. But I'm sure it's possible to make the numbers add up. And I'd imagine that SpaceX probably won't struggle to raise money for any reasonable idea they can come up with, given their past successes.