They base this trope on several false assumptions.
- Any science that doesn't make a profit and can't be funded by by a non-profit is not worth investigating. They typically bring up moralistic examples (research into the sex lives of animals).
- Business are better suited to decided which scientific endeavors can make a profit.
- Businesses care more about profit than about anything else, and therefore will investigate all potentially profitable areas.
Lets start with part 1. There are a lot of science that can't make a profit. I could talk about the endless number of orphan diseases (diseases too rare for cures/treatments to be profitable). I could also talk about the big science questions that require HUGE expenditures to answer - such as the age of the universe. These things are worthwhile even without a profit, yet for various reasons are not appropriate for for non-profits to answer. Among other things, sometimes these huge expenditures need steady funding that can't depend upon non-profit. Which brings us to part 2.
The biggest tech boons of the past 50 years derive from government funded initiatives. But there is a corollary to this fact, which is more importantly: There was nothing stopping businesses from doing the research themselves. The most obvious one is the internet, but the space program also counts. Business could have created the internet, but failed to step up to the plate. So businesses have demonstrated an INABILITY to fund key, profitable research.
Government uses different standards to decide upon funding than businesses do. Businesses do in fact make good decisions. They invest in a lot of valid scientific research, and ignore many bogus ones. But so does government - and more importantly government invests in different technology than business does.
Business has a rather short timeline. Small business has to make a profit asap. If they don't, they change their business model right away, and if they can't get a profit within two years, they die. Public corporations usually can't look further than 1 year, and die after six years or so of losses. Private business can look three-four years ahead but will die after ten years without a profit.
A lot of science however takes decades. Most of the twentieth century owes itself to the scientific work of Nikola Tesla. Make no mistake, Tesla made a lot of money - when he was young. But he gave up his patents to save Westinghouse (which failed to work, GE eventually stole them). But even after he lost the money, he proceeded to invent a multiple of advanced scientific devices, all of which took DECADES to become profitable. He made discoveries related to radar, microwave ovens, computers, and even VTOL airplanes. Business did not actually follow his research until decades after he died. They had their chance and failed.
Goddard did his first rocket work in 1926, but it didn't really become profitable until the early1940's when the Germans turned them into a viable weapon of war. That's more than a decade. Not to mention it took over fifty years from Goddard's first rocket to the big business of satellites.
The internet started before 1969, but it didn't become truly profitable until 1990, and internet commerce didn't start for another 4 years.
Lots of big, profitable science takes many, many decades to make a profit. That far exceeds the schedule that business uses. Worse, if you waited on these things, it would mean waiting for the results. Some things you need to pay to do asap. Which brings us to part 3.
Bad timing isn't the only reason why businesses miss profit opportunities. Businesses tend to be moralistic. They have to worry about PR and can't get involved in certain things. Banks will reject financially sensible loans because they don't want to get involved in sex businesses. Not to mention prejudice about gays, women, etc. Business can't research how ducks have sex, even if the biochemistry is incredibly interesting and can lead to real scientific progress with actual financial awards.
Sometimes businesses care more about security than profit. As in, they would rather maintain their existing business then try to create a better business model that undercuts their current one. Worse, they are quite willing to legal (and sometimes illegal) monopolistic tactics to prevent others from doing it. Look at Tesla and their business model. Existing large corporations undermine new companies research, just as they undermine new business models.
Why? Because the risk-reward is is MUCH lower to undermine something than to try something new.
People and organizations with large amounts of money care more about risk than about reward. Not that hard to understand, the more you have to lose, the more you care about losing it.
Governments have several specific immunities to this kind of risk. Usually they don't have to answer to anyone about specific programs - in part because they are often looked at as jobs programs, in part because they amalgamate so many programs that some are doing well even if some are doing it poorly. In the US, the government has so much money that even large science projects take up such a small part of the budget that no one cares if they fail.
For all of these reasons, government should continue to fund science. They don't always do it better than business does, but the different priorities of government allows it to make hugely profitable investments that the business world simply can not or will not make.
Now a couple of extra points.
- I am talking about funding science, not restricting research. Funding is good, restricting is bad. Laws restricting research is about picking winners and losers. They stop better technology by laws, not through money.
- Funding is not picking winners or losers. You can still win if your opponent is better funded. Just ask Nikola Tesla. General Electric and Edison had much better funding than Westinghouse and Tesla. As a direct result GE strong armed Westinghouse, but they ended up using TESLA's inventions. Nikola Tesla won the science, even if Edison won the money. While it might be unfair to Tesla, the country as a whole came out ahead, despite Edison's attempts to push into using the wrong technology.