When talking about research spending, you have to distinguish between basic and applied research. Government tends to fund basic research and private industry tends to fund applied research.
Basic research is science research done for its own sake. Discovering natural phenomena and the like to expand the frontiers of knowledge. Private industry doesn't do much of this anymore. It's clear whybasic research is costly and the results may never be commercialized. More importantly, the knowledge that comes from basic research can't be patented. Discovering something that exists in nature lacks the "inventive step" that a patentable invention must possess. Since anyone else can come along and use what you discovered, there isn't much incentive for private firms to spend money on basic research.
Applied research and development is the process of bringing technology to market and adapting it for large scale production. Applied R&D is what private companies spend on research. However without basic research done beforehand, there wouldn't be any new promising technology in the pipeline to try to commercialize.
So without government funding, you would still see innovation but it would be confined to applications of basic research that is already known. If you're adverse to the idea of the government directly funding research you can do what was done for AT&T. Monopoly status gave them enough profit to fund their own research at Bell Labs. Unfortunately,
Bell Labs stopped doing basic research when deregulation caught up to them. So despite having to pay inflated prices for telephone service, we did get innovations such as the transistor and the UNIX operating system out of them.