Let's deconstruct these assumptions:
"Baumol and Bowen pointed out that the same number of musicians is needed to play a Beethoven string quartet today as was needed in the 19th century; the productivity of classical music performance has not increased. On the other hand, the real wages of musicians (as in all other professions) have increased greatly since the 19th century."
1. Yes, string quartets still require four people.
2. This does not mean the "productivity of classical music has not increased", because:
a. String quartets can now make recordings and also play on radio/TV/streaming services, in addition to playing live. This means much larger numbers of people can hear a performance. This translates to ad revenue, streaming income, and sales of recordings. And there is also secondary income of various kinds for various supporting industries, including other forms of media.
b. String quartets can travel much larger distances than they used to be able to, allowing them to play live music over a much wider area than was possible when the fastest mode of transport was a horse. This hugely increases the possible listener base and potential ticket sales.
c. Culturally notable string quartets are likely to play in much larger concert halls than used to be the case, with increased direct ticket income.
d. The classical music industry is far more commercialised. There are numerous festivals and concert series which bring in far more money than they did when owning a pet orchestra was an eccentric hobby for aristocrats.
e. There are far more people than there used to be in the 19th century, and the worldwide classical music audience is much larger than it used to be.
So - this is simply a bad, ignorant example. It's not just wrong, it's flagrantly, wildly, outrageously misinformed, and is based on an almost total lack of insight into an industry that is worth $146 million a year - of which around $90 million is income from streaming.
The other examples are just as ridiculous and trivially incorrect. The productivity of nurses is not defined by the time it takes to change a bandage - ask any ICU nurse - and the productivity of professors is not measured by the time it takes to mark an essay.
How is anyone supposed to take this level of argumentation seriously when there is no evidence the authors made a credible professional effort to understand the economics of their own examples?
And as an advanced exercise for economists - how much has this poor level of economic insight cost the economy?