There is no proof for this, it's just something we like to say. There is also no real way to test it - Non competing versus competing? We can however look at historical and current examples. The Soviet Union led the space race, the Soviet Union made many innovations without the need for competition. Cuba has a higher life expectancy than the us and a stronger healthcare sector. China leads in published scientific journals. Both the Soviet Union and china eliminated famines. Both the Soviet Union and china drastically increased industrial productive capacity in decades - something that took capitalists more than a century.
Even if competition led to innovation, it also leads to incredible redundancy and waste. The idea that two people working against each other creates a better product than two people working with each other, is absurd. It has no basis in reality, it's just a vibes based thing we like to say. At best we end up with two similar products. Had they people collaborated we would have had the same amount of manpower focused on making one project - typically meaning higher quality, faster innovation. We highlight the times people choose to go against competition (The three-point-seatbelt, the Polio cure and insulin) as "good things" that had an immense influence. It is not a coincidence that when we choose to go against this competetive nature of capitalism, the gains are immense.
Competition drives specifically innovation that increases profits, which generally means making things more shit. Jeff Bezos innovated how to fuck over his workers so they could work harder for less. Uber innovated how it could fuck over taxi drivers. The tech firms innovated how to make walled gardens, and the hardware world at large innovated "planned obsolescence".

Germany's "social" market has a high amount of homeless people. It also has a high amount of underpaid immigrants being exploited for their labor. It relies - like all western capitalist states - on the exploitation of the third world as well.

[–] Kleysley@discuss.tchncs.de 1 points 1 year ago

The Soviet Union led the space race, the Soviet Union made many innovations without the need for competition

They were very much competing (against the USA) in the space race, why else would it be called a "race"? There may be no proof for my statement about competition driving innovation but would you just innovate for the sake of innovating without any rewards? I would not...

Also, I do notice that monopolies tend to be less innovative than multiple competing businesses in a market.

2.Agreed but if something is completely redundanty it will die out in a capitalist market and more importantly, what would be the incentive to innovate at all if we had one monopoly?

Completely agee on this one and I do think there should be regulations regarding the market (not like in the USA for example).

high amount of homeless people.

Because it doesnt work like its supposed to, but from a theoretical point of view, they all have the right to food and shelter and everything they need to keep their dignity...