The only thing that capitalism implies is the existence of a class that does not work, but collects profits from the capital it owns.

That class sees competition is an unnecessary, and a profit-reducing problem[1] that can be routed around.

[1] See Thiel's monopoly essay.

Instead of aspiring to be capitalistic we should aspire to have a competitive market economy.

> Capitalism sort of implies competition...

Actually, I don't think it does:

https://www.lexico.com/en/definition/capitalism:

> An economic and political system in which a country's trade and industry are controlled by private owners for profit, rather than by the state.

A privately-owned monopoly that ruthlessly crushes all competition is just as capitalistic as a privately-owned competitor in a market with perfect competition. The key concept is private ownership and control, not competition. Competition is is only required if you want the resulting system to have some positive externalities for consumers and society at large.