I know you asked for one, but that is about impossible to do.. It would come down to two products anyway: Super TLP, and Element 8.
1) Element 8 works for just about any residential or commercial job. It won't get all of the really tough stuff (bad grease and petroleum products) but will get most. You can boost it with a citrus solvent and it is darn near perfect. I use it as a pre-spray and rinse with it. What residue it may leave (mostly if used to heavy) is a light powder that will vacuum away.
2) Super TLP from Accelerated Chemical Technologies (Duane Oxley.) It is a blend with a Solvent in it, and will will get just about anything. I use it as a pre spray and rinse with clear water or Ultra Rinse.
3) Clean Streak. This is a powder from Duane that we use for restaurants and really bad commercial work. With a shot of citrus solvent, there is not much of anything it won't touch. If you like Power Burst, then you will LOVE this stuff! (Yes, I've used Power Burst too.)
4) Ultra Rinse (from Duane, again) as our rinse agent. I use this following Super TLP and Clean Streak. It is an acid rinse, but contains more than just acid. I'll explain this in a minute..
5) Citrusolvit for a booster (also from Duane.) I add a little of this whenever there is a B A D case of grease, or if there is a petroleum product on the carpet, or for such things as tape residue. All of the above work so well, I don't need much of this. The above also almost eliminate the use of spotters. The only spot cleaners I really use are red relief, stain magic and a solvent spotter for getting those bad greasy spots (usually petroleum based) and ink, etc. that you "uncover" as you clean.
I always start with the least aggressive chemical needed. After a few years of this, I can look at the job and know which cleaner I need. While there is more than 1 listed, I will rarely have to use more than one on a job. After YEARS of trying stuff, these are my staples. I know that if I can't make any carpet look good with these, then it is pretty much so time for replacement. As you see, there are 3 pre-sprays, 2 rinses, and a booster (Element 8 acts as pre-spray and rinse.) The reason for using an acid rinse comes down to pure chemistry. An alkaline cleaner (pre-spray) will break down the organic soil. The acid rinse will break down the inorganic soil, as well as facilitate the removal of the pre-spray.