Although I think that there're still a few tweaks that could be made to the tech tree, fundamentally I think it's a good system.
I have to say, I'm not a huge fan of randomness in the research trees, as I don't think it reflects the concept believably. Research is normally a directed, focused and ordered thing, and while occasionally discoveries are made that are not exactly specific to the purpose of a particular research, I'd not go so far as to say that researching for something specific and making a side discovery will always or even mostly result in the abandonment of the initial target.
I respectfully disagree. With a few notable exceptions (mostly military hardware), little to none of mankind's technological breakthroughs took place at the behest of a government. Ultimately, from the perspective of a ruler, you have little to no direct control over most research, as it is mainly taking place amongst the general populace (including corporations here).
One concept that I've been toying with for a while would be a research system that truly embraces the cliche, "necessity is the mother of invention." As situations cropped up, the vast majority of research would be taking place automatically. If, for instance, your nation experiences repeated droughts, you might unlock the "irrigation system" technology...