The pricing of a swap didn't first order really reflect credit risk of the swap itself (that effect is small versus what we are discussing here). Because swaps between dealers have long been collateralised with mutual mark to market. It did reflect the fact that LIBOR is rate for an unsecured loan between banks. Possibly the new regime caps how high that might go, but it's really less about LIBOR and more about Treasury funding.
Capital requirements and the higher cost of balance sheet as reflected in the repo market must be a starting point. And that's not just a US thing, but is at work in other markets too.
The only way to deliver a Treasury is with a Treasury, which you have to track down out of inventory or from another dealer. You can write a swap without having to go through that ordeal. This means lower transaction costs.
Compare this to before, when swaps were often un-collateralized, so you might have a huge paper profit on a trade that you'll never actually realize because the counterparty lacks the cash to settle up.
So before, you could lose the total amount of your trade, but now you can only lose a day's worth of gain or loss.
This is a big improvement, and the risk to the taxpayer is pretty de minimus. Of course the central clearinghouse could default, but that's very unlikely for a variety of reasons (mostly that the central clearinghouse's whole reason for existence is not to default).
I don't know the mechanics of swap settlement well enough to understand if that is correct, but it seems plausible.
Suppose you're a rates dealer. (Rates dealers buy and sell Treasuries and swaps, amongst other things.) An investor wants to invest at the 10-year rate. Say they insist on getting this in the form of a U.S. Treasury. You must either (a) buy a Treasury on the market or (b) pull one from inventory. No other options. Say, on the other hand, they are open to dealing in swaps. You could hedge this like a Treasury. You can also hedge with another swap. Two options instead of one. Makes your life easier, doesn't it?
Dealers always preferred swaps. But investors didn't like taking on the counterparty risk. Dodd-Frank changed that. Now swaps are mutualized. If you take out a swap with JPMorgan and they go kaput, other parties will pool together to make you whole. Less of a difference, in terms of credit quality, between a swap and a Treasury now. Dodd-Frank also made it more expensive to hold Treasuries in inventory.
In summary, swaps were always tastier to dealers. Dodd-Frank made them more attractive to investors. At the same time Treasuries became even less fun for dealers. Left hand meets right hand and you get lower fees on swaps with a commensurate shift in net pricing.