Except there's no nation-wide drive to be "number one" - except for maybe the US but then again they use that to cover up how shite their QoL is.

Progress on a societal level is made once it happens on an individual level, and society recognises the worth of that progress. See e.g. bicycles, cars, telephone, radio, electricity in general, vaccines, or pasteurisation, or literally any advancement - a personal need (let that be for the thing, or for knowledge) drives the individual discovery, which then gets adopted by society.

In fact you can see contrary examples of the "free market" not innovating but keeping innovation away from people. Not just today, but look back e.g. at the various industry battles that resulted in not the better product but the better capitalist winning. Edison v Tesla - even though we use mostly Tesla's work today, it's credited to Edison. For example, Tesla always promoted AC, while Edison was a proponent of DC. Guess which we are using today overwhelmingly? Guess who got rich, and who died penniless?

The free market isn't the source of innovation, it's the stifler of it. Period.