Let me say I am not a pilot but I have some general engineering background and some interest in aeronautics. So my answers may not be all accurate, but the general gist should be right.
I am pretty sure you are thinking about an airspeed meter the way most people would think about it - a small turbine wheel in a tube that rotates faster the faster air passes through the tube. Unfortunately, these devices do not function well at high altitudes, low temperatures and high airspeeds - apart from ice formation, one of the biggest problems is that the outer edge of the turbine would actually move at supersonic speed.
The airspeed meters on commercial planes thus use a different system - they measure the pressure of oncoming air in a closed tube. The higher the pressure, the faster you are going. However, this also means they need to be calibrated against the ambient outside pressure which is where they become impractical rather quickly for emergency deployment - you need the meter to get an electronic signal from an altimeter to calculate your speed right. A mechanical meter would require setting the scale first or reading across curved lines, both highly difficult if you are in an emergency.
Add to that the problem that airspeeds have a low tolerance limit at high altutudes - too little and you don't have enough lift, too much and the plane will suddenly lose all lift and may even sustain damage. Each plane has its own set of allowable speeds for each altitude (lower flying allows a wider speed range). In heavy turbulence, over- or undershooting these speeds is a threat and planes suddenly losing significant altitude in a turbulent area often cause this through excessive or insufficient speed.
Modern aircraft do already have multiple (usually three), independent airspeed meters at least one of which should be operating off a battery-backed voltage source. They also have a mechanical instrument called artificial horizon that does exactly what your two spirit levels propose to do, in a way intuitive to a pilot.
Thanks to all these backups, it is exceedingly rare for a plane to go down because of a single failure - if a single defect causes a crash, it is usually a structural one (like the Concorde disaster where the plane ripped a fuel tank). Flight losses like the recent Air France 447 accident are the result of multiple equipment failures adding up to a deadly cascade - this is also why nearly all recent aviation disasters either involve pilot error/misjudgement, intentional sabotage/terrorism or a previous maintenance error as well as a random, normally easily compensated for, problem.
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