Consider doing the math on how many paid users need to exist to subsidize each free user. Suppose each free user uses, say, 20% of their space and does every single available promotion, yielding 20GB of space. This means each free user uses 4GB (a huge overestimate, I suspect.) This means that given S3 storage rates (and if Dropbox doesn't have better than the public rates, they're doing it wrong), each free user costs Dropbox $0.22 per month. Let's say that each paid user uses half their space, and that all the users are only using the 100GB plans. Then paid users cost them $2.75 per month. This also assumes that absolutely no data is deduped.
Now, let's assume that Dropbox pockets a quarter of the money to pay salary, other business overhead, and so on. This means that Dropbox needs a conversion rate of about 4% to be profitable. Sounds completely reasonable and sustainable to me, especially given how generous my storage numbers are.
It is cheaper to store 100GB in Dropbox than to store your own 100GB in S3. It would cost $12.50 plus transfer costs to use S3. It costs $9.99 and no transfer costs (besides your own net access) to use Dropbox. Dropbox is storing a lot more than 100GB, so they get bulk prices.
That's not a solution, it's a design tradeoff. Dropbox's servers are the "truth", and the software's clear goal is to get a copy on the servers. There are many reasons for this--weird conflicts, inconsistencies, and so on--that are much harder to resolve than if there is a copy on the servers.
Once that happens, other clients will ask to download from the servers, notice that it's on the LAN already, and take it from there. I bet if you install a new client on the same LAN, or share a folder between clients on the LAN, or add a folder to selective sync, once the files are already there... it will be a competitive speed.