Power race didnt help the OG Xbox, but it did help the OG PS2 against the Dreamcast. Xbox came out almost 2 years after PS2 came out in Japan in March 2000. By the time Xbox came out, Sony had effectively killed Sega.
Power race did help the Xbox 360 attract the hardcore who in turn attracted casuals and made it the defacto console for CoD. Granted it was also exclusives, but every single game for the first few years ran better on the 360.
Power race helped Sony win the generation after a relatively lean first few years. It was not the only cause, but it definitely helped.
Power race this gen didnt materialize because MS had a retarded console that they overshipped while undershipping the so-called most powerful console. Not to mention, completely botching the launch with poor performing launch titles. Had they focused on one console and managed to ship a decent amount of units of that 12 tflops console, things might have been different. Especially considering just how no one could find the PS5 in the early days. The only console on shelves was the 4 tflops shitbox and no one wanted it. That 12 tflops XSX was a great fucking console despite the early issues and would've at least helped them keep up with the PS5 had they focused on shipping more than the PS5.
And lastly, and Nintendo fans dont like to hear this, but the power race effectively knocked Nintendo out of the console market. They realized they couldnt fight the power war and literally bowed out making handhelds literally 2-3 gens behind in power. Yes, they are selling more than ever, but they dont have the massive piece of the pie Sony and MS carved out of these massive CoD, Fifa, Madden, AC, RDR2, and GTA releases. Because they simply couldnt compete on power anymore.