Based on what I've read from people vastly more informed than me, this absolutely 100% seems to be the case.
Even beyond that, the general impression I get w.r.t stuff like supermaneuverability is that it's a much better use of money to ensure that most fights never even make it to the point where the stuff like the cobra seems like a good idea. Given the choice between 1) "marginally improving survivability in comparatively low-energy corner-case states" and 2) "increasing the odds that the fight never makes it to the merge," #2 seems like a much better choice in terms of money spent and pilots kept alive. (Though a counterpoint, I guess, based my my casual understanding, would be that making the judgment too heavily in favor of #2 was part of what hampered the USAF and Navy's air-to-air combat capabilities in Vietnam)
Air combat is rarely 1vs1 so being slow means you get killed by someone else.