There was the pride element to consider. An SST to match the best American one would be something to be proud of--an SST where the Americans have none? How could that be cancelled?
Subsonic with better economy is clearly the path of profit--we know now, in retrospect, in part because there were two ventures to develop SSTs in the '70 and both failed to do more than be an outlier capability that never came close to a real profit maker. But profit for the sake of profit is inglorious--in the long run, when your sensible firm is still standing and your rival is bankrupt and gone, and nothing challenges your far more economic subsonic planes in the realm of speed, you may smirk. But for a while there, you are being boring and they are being cool.
Perhaps indeed the key would be for Boeing to keep going, or give the US SST contract to Lockheed, or something.
A couple technical matters--Concorde was designed around Mach 2, and this was the maximum speed at which the major airframe could still be aluminum with only a minority of critical parts make of titanium or high temperature steels. Playing this glory game, the US taxpayer subsidized Boeing plane was supposed to both be larger, and achieve Mach 3 cruising speeds--had it been feasible to do that, clearly the Concorde would be relegated to secondary markets while the faster and larger American plane would take over the plum routes.
It might have gone in another direction--Barnes Wallis suggested first developing a somewhat slower than Mach 2 plane, somewhere around 1.5-5/3 or so, such that full shock heated stratospheric temperatures would be well below those that soften aluminum, say in the comfortable human temperature range, 30 C or so. If that were the never-exceed maximum then it would be possible to make the whole plane out of traditional materials--for a variety of other reasons too the basic task would be easier. Engines would be closer to those already available off the shelf for instance; air intakes easier to design, etc etc. Such a plane would be significantly faster than the best subsonic plane (Convair made the fastest of the first generation planes of the basic 707 layout, along with the DC-8, but never managed to sell many). But it would be far easier to develop than the Concorde, much much easier than the American 2707. It could operate on shorter runways. It could get to market much earlier than either of the more ambitious models. Probably such a "modest" project would not be sufficiently exciting to be the basis of a trans-Channel project, and either British firms or French, or possibly both in hot competition, would pursue it--indeed that was happening on paper in the period the two firms allied. Again the fear was, make a plane that works at Mach 1.65 and then when someone comes along with a Mach 2.4 version you are screwed--the perception was that the latter would be along in six years or so.
So--maybe if the Americans were more gung ho but also chose a slightly more modest target--say Boeing still gets it but the goal is "merely" Mach 2.3 or something like that, but bigger than Concorde. They get started on it and seem to be making progress while the Concorde deal is still being negotiated; the Europeans look at Boeing overtaking them and shudder and back out, going their separate ways. No Concorde because they are scared off. Then around 1967 or so it becomes evident that the Boeing project is actually not going that well. It turns out to be a lot more expensive to do Mach 2.3 than they thought and they consider whether to trim back to Mach 1.9, double down on R&D costs and bull through, or pack it in.
The longer they keep dithering and sending good money after bad, only to be finally shut down by the sonic boom protestors, the longer European firms are deterred and maybe forced into the weary, stale, flat and profitable fields of subsonic improvements, then around 1970 a bunch of accumulating economic woes leave darken all investment horizons and leave the western world with no SST. It is an interesting sideline whether Tupolev develops their entry or not.