Ultimately, we will never know
BA, so we can't really say if a Boeing or Lockheed SST would have failed commercially like Concorde did. If two countries (free world countries anyway, not ignoring the Tu-144, but that design had more problems) had developed SSTs, then their respective governments would have been more likely to embrace the concepts and cut some of the red tape that Concorde encountered later in favor of the all mighty dollar (or pound sterling). Afterall, a US built SST would have resulted in more jobs for the people and another product to export. Concerns over environmental damage from SST noise and sonic booms would have probably been more muted (though still there), so such SSTs potentially could have been employed on more routes then what Concorde ultimately wound up with.
As it happened, certain problems with 2707's design and budget ultimately killed it. Later engineering analysis concluded that the plane could have flown with the swing wing, or passengers, but not both. So the thing went through a major redesign to something that resembled the Lockheed concept more (but with a tailplane and elevators on it) and a second mockup was made before the project was scrapped. Now if Lockheed's design had been selected instead, I'm betting it would have made it into production, but again we shall never know.
The other problem was that by the time the 2707 got close to having metal cut for it, the presidential and congressional administrations had changed from ones that embraced such bold concepts in the 1960s (SSTs, Moon program) to cutting budgets in the 1970s. Usually these days a government official doesn't want to back something unless they see immediate gain while they are still in office, lest they get voted out and their successor/opponent takes credit for it. Kind of hard to do that with a project that takes about 6 to 10 years to get from drawing board to airline service.
So, Concorde became the only plane and orders for it dried up when the US announced their SST effort, but the US SST never materialized. Still, Concorde orders never really rematerialized, probably due to the budget crunches of the early 1970s and the glimpse of things to come in the form of the 747. Add to that, the UK and France were alone in their route proving of Concorde and had to deal with the environmental lobby in the US who blocked Concorde from landing at
JFK for the longest time and SSTs as a result were perceived as expensive and political hot potatoes by the time Concorde was ready for service. So, no additional orders and no work done on a proposed longer range Concorde-B with increased fuel and better engines and we are left with the fleet we got. If the US had an SST, chances are that it would have been the more "in" thing to get and the environmental lobby would have been vocal, but that is about all they would have been. Also, with two competing SSTs, you would then have a competitor in the market, thereby lowering unit costs as a result, making it potentially more lucrative to customers wanting to sign big contracts. In a sense, it might have started the Airbus/Boeing war about 5 years earlier with the SSTs being their flagship products.
But, like I said we will never know. It falls to the next generation to come up with the next SST and hopefully one will be flying before I make my unplanned trip to the next level of existence. As for PTVs, Concorde became a trip experience in and of itself, so PTVs were never really part of the equation. If a larger SST were used on Pacific routes, where even at Mach 2.7 the travel could take about 5 to 6 hours, then I could see it. But not for a three hour hop over the Atlantic.