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A methalox engine is fed from two cryogenic fuel tanks. Why can't the methane and oxygen be mixed as gases, in the desired proportions, and then chilled to a temp that liquefies both? From a single tank a single turbo pump could then feed this into the combustion chamber (part of flow going thru the nozzle cooling channels). Yes, a bit of same mix would be tapped off to power the turbo pump.

Saves the weight of tank bulkheads, separate plumbing, reduces turbo pump complexities. Must be a reason or the rocket scientists would already be doing this, but would like to know what it is.

Edit: Thank you to all who answered. Even the imperfect answers helped, as the comments helped me work through the whys and wherefores. I did know a methalox mixture, if it could exist, would be highly dangerous, but unsure how dangerous compared to a failure/fire of one tank causing the other tank to rupture, mixing the two. Even I can now see why the rocket scientists got it right.

Urged on at a similar question on Chemistry SE, it seems that the idea of mixing liquid oxygen and liquid methane is an old one. And one that, using some of the answers above, seems to be cloaked in at least some hyperbole.

Of relevance is R.L. Every and J.O. Thieme, Journal of Spacecraft and Rockets 2(5) 787-789 (1965) titled "Liquid oxygen and liquid methane mixtures as rocket monopropellants". In the introduction the authors note that previous work shows that the liquids are miscible in all proportions above 90K. Their tests show a specific impulse of almost 300 sec, and an exhaust velocity near 6000 fps.

In addition, since "shock sensitivities were reported" in the earlier work, they did some, well, vaguely disturbing experiments (hey, it was the 60's). "Tests were conducted to determine whether violent stirring or agitation, as found in an impeller-type pump, would detonate the mixture", although they didn't have any explosions there. They then went on to quantify the impact sensitivity, dropping a weight onto a stainless steel beaker of different liquid mixtures from increasing heights until an explosion occurred. Impact sensitivities of 20-60 ft-lb were discovered (these experiments were performed with open beakers of the cryogenic liquids, with light from the room shining on them - hence the hyperbole bit). They also looked at adiabatic compression as a cause of explosion and found the liquid oxygen/methane mixtures were safer than some other things like nitromethane (which really isn't that comforting).

So, it would appear that the idea of using the liquid mixture as a monopropellant isn't totally off the wall, but please do it somewhere far from me...

To quote John D. Clark's great book Ignition! (Chapter 11: The Hopeful Monoprops):

If Tannenbaum's mixtures were bad, that proposed at a monopropellant conference in October 1957 by an optimist from Air Products, Inc., was enough to raise the hair on the head of anybody in the propellant business. He suggested that a mixture of liquid oxygen and liquid methane would be an extra high-energy monopropellant, and had even worked out the phase diagrams of the system.* How he avoided suicide (the first rule in handling liquid oxygen is that you never, never let it come in contact with a potential fuel) is an interesting question, particularly as JPL later demonstrated that you could make the mixture detonate merely by shining a bright light on it. Nevertheless, ten years later I read an article seriously proposing an oxygen-methane monopropellant! Apparently junior engineers are allergic to the history of their own business.

In addition to what the other answer said, it would take very little provocation for such a situation to turn into a good way to test the blast resistance of nearby facilities.

At STP:

• LOX's boiling point is 90.19 K
  


• Methane's freezing point is 90.7 K
  

This does not a priori prove that a solution of the two can not exist. However it does mean that they can not be handled as liquids at the same temperature, making mixing the two more difficult.

And so I've just asked Can a stoichiometric mixture of oxygen and methane exist as a liquid at standard pressure and some (low) temperature?

We know that liquid air exists which shows that LOX and LN2 can mix together. But methane is an organic molecules and we know that heavier $textC_n textH_2n+2$ hydrocarbons include oils and waxes don't like to dissolve in non-organic solvents.

The argument against premixing is the danger of ignition due to a spark or tiny localized generation of heat. As @Tristan and @PearsonArtPhoto both mention 1, 2 the SpaceX explosion "fast fire" occurred because of the presence of a combustible material in direct contact with LOX and a localized source of mechanically produced heat. See this answer and note that the situation is discussed at length in Scott Manley's video The Dumbest Mistakes In Space Exploration

Also watch the video below, discussed in more detail in Why doesn't carbon fiber overwrapping in LOX catch fire? (watch this video first)