And what would take their place? When companies pay people to think up great new ideas, they want to get something in return for the investment - that won't change no matter what government does. With patents, one way to get a return is to patent the ideas and sell products that use them. If you eliminate patents, imagine an investor considering funding research. She will think, "I could incur the cost of paying for the research and then sell the products. But then other investors will simply be able to begin manufacturing and selling the products without having to pay for any research. I'll just let someone else pay for the research and invest in a factory once the technology has already been developed."
See the problem? The investor paying for the research will be worse off than the rest of her peers. Like all humans, investors are trying to benefit themselves, so they'll wait for someone else to make the sacrifice.
This is a possible scenario, but there's another - perhaps more likely - outcome. With patents gone, investors continue to fund research but use a different device to increase return on investment: secrecy. Technology is developed behind closed doors and hidden from the public. This might mean products whose inner workings cannot be hidden are less likely to be sold on the market, or that the ideas are cloaked within a bigger product (say, a new device for a car). In the former case, the public doesn't benefit at all, and in the latter case, the net effect is the same as patents, except that there's no deadline for them to expire.
I am NOT saying that all technology and great ideas spring from capital investment or the pursuit of greater personal wealth. I am NOT saying that the patent process is perfect by any means, or that patents do not cause harm. There *is* a cost to giving the developer of new technology a temporary monopoly on that technology.
But what is undeniable is that *some* good ideas and technology are made possible by people selfishly trying to become wealthy. Patents give people a selfish reason (and everyone is selfish to some degree) to think up great ideas and, importantly, publish them to the world; they also ensure that the monopoly will run out eventually (which isn't necessarily the case with secrecy).
There has to be some balance between the benefits of patents (more research) and the harm of patents (temporary monopolies). Eliminating patents will at best force entrepreneurs to use secrecy instead of patents; at worst, it will cause selfish people to go from doing research to doing something that is less beneficial to society but more lucrative for them. You can get rid of patents, but you can't get rid of selfishness - and our laws should reflect this.