I am starting to see where a compromise can effectively come into play that will make the game better for everyone.
Make the base tree non-random, shown techs AND some random "spice techs" that are still shown (like playing a game of Civ4 in which philosopy appears only 1 in 4 games). I imiagine spice techs will be crazy stuff like derigibles, blunderbusses, etc. Good times for all.
Make it so that there are certain "Field" techs that require an investment and give random bonuses. "Civics" "Philosophy" "Research Methods" and "Art" are all decent examples. These techs would be the more theoretical stuff, ie funding an academy of the arts will likely give you something good, but god knows what it will be.
Once a line on the base tech tree ends (ie on the weapon tree youve researched all weapons and known weapon based techs) you are given an option to simply invest in it and hope for the best. The fruits will be stackable (ie +1 sword) but random in what they are, with completion time related to benefit (ie better advantage, longer research). This is an infinite tech tree, and the system can balance itself. The "randomness" will be heavily weighted against things youve already got bonuses for, so your +4 swords mean that sword research will be both longer and less likely. This creates a system in which your rewarded for your calculated investment without knowing what it is.
The simple truth is that FULLY random techs, while I would love it, would probably create too many "OMFG gaem h8s me!!1!" posts. FULLY revealed and planned tech tree is however dull, and can never be infinite, unless stardock has some kind of awesome program that creates a never ending line of techs without overloading your PC, lol. Thus the best option is a mix, and I like the one described above, though my bias should be apparent. 
Anyway, hopefully a year long beta will create a system beyond any of our puny dreams.