As I have stated before on this site, terms like "molto allegro" were never intended to convey an exact measurement of beats per minute.
Verbal descriptions of tempo, like "allegro", "adagio" and "andante", were used by composers in previous times before the invention of accurate machines that could measure beats per minute. These verbal descriptions are nothing more than approximations. Mozart composed his music before the invention of the metronome.
The metronome, which can be set to beat out a specific number of beats per minute with accuracy, was patented in 1815 and quickly became popular. After that time, composers began to label sections of their music with a precise measurement of beats per minute if they wanted to, and they began to rely less on verbal descriptions like "allegro". If a composer after around 1820 continues to use words like "molto allegro" then that means that the composer wants you, the performer, to make your own decision about how fast to play it.
In classical music, the notes on the page are there for you to play precisely, but the tempo and the phrasing, and the speeding up and the slowing down when you see markings like "accelerando", "ritardando" and "rallentando", are there for you to interpret as you see fit. This is what makes classical music interesting -- no two performers (if they are musically adept) will play it exactly the same way every time.
Footnote: My favorite tempo marking in classical music is Beethoven's Mass in C, Opus 86 (1807), first movement, where Beethoven's tempo indication is "Andante con moto assai vivace quasi Allegretto ma non troppo."
That translates to "Andante with motion, almost like a very lively Allegretto, but not too much."
Not long after Beethoven published this piece, the metronome was invented and became popular. My suspicion is that everybody decided that it would be really useful to have a means of measuring beats per minute accurately if composers were going to go on like that!