The broken window fallacy is a controversial axiom that implies demand generation isn't a meaningful way to increase GDP (it comes from the camp that believes output capacity is the only true measure of GDP).
This concept became particularly controversial during the Cambridge Capital Controversy [0].
If you believe that GDP is an exogenous measure of what society can produce, you run into oddities like global GDP changing trajectory in 2008 [1] (i.e. we never 'caught up' but did the US housing crisis really cause the human race to lose our ability to create more goods and services?).
On the other hand, if you believe demand drives GDP, then why don't we just demand ourselves into more wealth? Shouldn't natural constraints like resource scarcity then drive GDP (i.e. the original underpinning of the broken window fallacy)?
In either case, the broken window fallacy is far from an agreed-upon axiom.
If I understand your point, the broken window fallacy is to say that a child who breaks a window has actually done something good for the economy by keeping glass makers and installers employed. Obviously this isn’t true because those people could be building new things instead of fixing the old.
Well, a huge portion of our economy is in fixing the old. Why waste so much money on healthcare for humans when we could use it to build bigger and better things. We have whole portions of the economy like food production whose entire purpose is to keep people alive. What a waste. The far more efficient option is to eliminate those people and let machines do the work. Even if GDP goes down, ultimate productivity goes up.
The same can be said for entertainment, hospitality, most education (we spend 20+ years educating people before they can meaningfully contribute) and marketing. A broken window theory might say these industries contribute to the economy and give people jobs, but actually they accomplish little.
