I guess it depends on what you consider to be allocatively efficient. Is it allocatively efficient that half of the food produced in the USA is wasted?

As for innovation/competition, Marx did recognize the role that competition played in driving innovation under capitalism, but capitalism also is unable to sustain competitive markets. After a while, somebody or a small group of people "win" the market competition and you end up with oligopolies/monopolies where the laws of market competition no longer apply in the same way. For example, the US food market is sewn up between a few megacorporations who collectively own most of the food companies in the USA.

There is the telecoms industry, the auto industry, and of course, finance. Globally, market competition is not the norm. A network of 700 corporations collectively own 80% of the entire world economy.

Of course innovation is a constant throughout human history (the rate of innovation has been doubtless highly variable, but innovation itself), and market competition is just one way of boosting it. In reality, many companies today are actually unwilling to make the big up-front investments needed to drive science and technology forward and are in fact reliant on government research or government funding to keep researching and innovating. Big Pharma is an excellent example of this. The Internet, which has been a fundamental game-changer for commerce, science and technology, was a government research project. And so on and so forth. Scientists themselves are explicit that public funding for research, rather than market forces, are crucial to drive their disciplines, and human technology, forward.

Some of the biggest game-changers in terms of science and technology did not come from companies pursuing profits but came from outside the sphere of market competition. Einstein worked out his early big breakthroughs, including his proof of the atomic theory of matter and special relativity, in his spare time as a patent clerk. These laid the basis for him to work out his really big breakthrough, general relativity. All three have fundamentally reshaped the course of science and techological development across the 20th century.

And, of course, a lot of scientific research has always been carried out at universities. Businesses benefit from publicly funded university research but do not contribute significantly to it.