Yah, if workers own a tiny portion of the means of production, as they do now in various co-ops around the globe, they will be either (1) required to operate on the basis of profit in order to outcompete entities that are not worker-owned, or (2) cease to exist because they get outcompeted by those who operate on the basis of profit.
This forces all existing co-ops to behave in line with capitalism as a whole. The point is to overcome that system of socio-economic relations: When calls are made for workers to own and operate production, as in this meme, they mean that the class constituted by workers — the proletariat — should be in control of all productive means. Not just that some workers should start co-ops, for this primary reason.
The idea that owners would sacrifice their profits if their business were merely a co-op is, I agree, not necessarily true. (Though workers in co-ops who are directly connected to the point of value production would definitely be more willing to sacrifice profits for decisions that enhance social value.) The point, however, is to move beyond an economy owned and operated for profit and forge a society in which profit is not the basis for operation in the first place. If, for example, workers' needs were guaranteed, the impetus for profit-seeking would evaporate, though will not be absent, at least while the artifacts of capitalist society persist in us and our institutions.
Allowing capitalist relations to persist, even if basic goods like food and homes were nationalized, enables a society in which capitalist profiteers continue to operate. History shows pretty explicitly that Capital will use the levers of power that exist, like The State, to eat away at or overturn any socialistic advances. E.g., suddenly the luxury capitalist corporation that sells idk, pearls, is lobbying (bribing) their way into privatizing beaches from which they operate. Slowly but surely the socioeconomic relations produced under capitalism foment and claw their way back to their former position. This requires a constant, indefinitely revolutionary society to keep capitalist relations at bay; that sort of momentum is not possible to sustain, certainly at the current moment.
It's necessary to abolish capitalists as a class because leaving capitalist systems of relations alone enables them to continue to re-produce themselves.
That doesn't preclude this sort of dual-economic setup from being a good thing, just insufficient.