There is one thing that brought me this question. Well 2 actually. First off is Wim Winters and his Authentic Sound channel where he argues that Beethoven is using double beat for his tempos. He relatively recently made a series of videos of a supposedly tempo accurate performance of Beethoven's Fifth. I can tell you from listening to a snippet(I didn't even get to the development section, it was so horrid) exactly how he got that tempo. He took a recording and then manipulated it to be slower. But even if he did use notation software and got a better sound out of it, I would still take issue to the slowness.
The second thing that brought me this question, also from Beethoven's fifth, is this tempo marking:
If I were to interpret this straight as half note = 108 BPM. I would then get quarter note = 216 BPM. If I were to interpret the tempo this way, it would be way too fast, even compared to the fastest performances of the piece(which for reference, are around 160-170 BPM). 216 BPM is Prestissimo these days and was probably Presto agitato in Beethoven's time. In the case of Mozart, I can understand why his Allegro molto is so variable, from 140 BPM to 210 BPM. But didn't tempo start getting standardized in Beethoven's time? Wasn't it clear at that time that 210 BPM is not any sort of Allegro? In that case, why would Beethoven write such an outrageous tempo marking for his fifth symphony?
Double beat interpretation
Now we come to Wim Winter's interpretation. According to him, the whole symphony is supposed to be interpreted as though it was in 4/4 time. Given that 2/4 and 4/4 are very similar in terms of accent, this isn't out of the question. What is out of the question, is once again, the resulting tempo. At a tempo of quarter note = 108, sure you could say it is Allegretto or maybe even Allegro. But that is too slow for Allegro con brio. Con brio translates to with energy and in the case of tempo, implies that the tempo is faster than averages for the marking.
So in other words, Allegro con brio implies a fast Allegro. The slowest performances of Beethoven's Fifth tend to hover around 132 BPM, certainly faster than the average of 120-125 BPM for Allegro. 108 BPM is nowhere near Allegro con brio. This alone makes me seriously question the double beat interpretation of Beethoven's tempo.
It can't just be that Beethoven's metronome was broken. If that was the case, I would expect to see something more along the lines of Adagio half note = 120 and I don't. But neither the straight interpretation or the double beat interpretation is right either. So why is Beethoven's tempo so off from ours?