Yeah, there's a school of thought that competition, fares, and cabin service would all improve on American carriers if we allowed fifth-freedom flights
within the U.S. Imagine if you could buy a seat on the Qantas 747 JFK-LAX — why would anyone ever prefer AA/B6/DL?
On the flip side, things for travelers might also get worse, or even more "low costy", if we had domestic fifth-freedom flights. In order to compete with European low-cost carriers, Lufthansa migrated a lot of their intra-Europe flights to low-cost affiliate Germanwings, whose travelers don't get the same perks or lounge access as people on normal LH flights. This has been kinda a pain.
But competition can be good. One nice perk of the Norwegian Air incursion into the transatlantic market has been the ultra-cheap Star Alliance retaliation fares to Northern Europe airports that DY serves. There are some amazing $500–$600 round trip fares from either coast to OSL, and you can turn them into a trip to "anywhere in Europe" by using stopovers wisely.
This article mentions that the Azores are another potential hub for low-cost carriers but doesn't mention that SATA (S4) really does publish some dirt cheap fares to Europe, BOS-PDL-LIS at like $300ish round trip, albeit on a sketchy A310 aircraft with low-cost service.