Trickle-down economics fantasy doesn't work because self-interest results in trickle-up.
One issue really is that there is an apparent lack of valuable, human-doable work to go around because of automation and a highly-connected, globalized world.
Zillions of us are basically working partial shit jobs because either employers don't want to pay benefits or there's no need (low demand/oversupply) for more skilled workers, but the university machine keeps cranking out overqualified people and plunging them into desperation of debt. Many times more entrepreneurs and support thereof are needed to create some decent jobs, because human ingenuity and capability is being left to rot in a fry cooker. (Edit: Investing/mentoring/etc. are hard-to-scale activities except perhaps socially, but they need to happen to utilize more people overall which can be paid more individually and could be where most wealth is created... not as many giant businesses but comfortable cash machines.)
>there is an apparent lack of valuable, human-doable work to go around
No, there's a lack of immediately profitable human-doable work to go around, and markets don't have the rationality or intelligence to invent mechanisms that guarantee it gets done as it should.
US infrastructure is falling apart. Health insurance is run by vampires. [1] Care for seniors has huge growth potential. Defence spending is one big F-35. Education at almost all levels is far behind where it should be. There are many areas where housing is unaffordable, and a housing program could fix that. Climate change mitigation is definitely going to need to become a thing.
Etc.
There's no lack of work that could be done. The problem is that the standard markets-ra-ra-ra ideology is too stupid and myopically self-interested to understand that sometimes lower profits and higher taxes in the short term can lead to much bigger profits in the longer term.
Addressing most of your laundry list will not result in discernible added value. We can add arbitrary effort to the GDP to make the GDP grow, but we may have already seen all the benefits of that effort by the time it's measured.
The best examples you listed are infrastructure and housing. Both are valuable, assuming we build the things people actually want or need. But, again, we could build a thousand bridges to nowhere and a million new housing units in Detroit, boost our GDP, and waste money in the long run.
Senior care, education (qua education), and climate change mitigation are not obviously profitable, even in the long term. Maybe they're good, but good doesn't address the lack of wage growth for the under-four-years-of-college set.
I'm not sure that infrastructure projects need to be bridges to nowhere or housing in dead cities to be useful. There are plenty of infrastructure projects to be done in vibrant, growing cities/regions. Overdue road repair/maintenance, water and sewage modernization, park updates, library modernization and so on could do a lot with long-term benefits. Fiber as infrastructure has some promising potential (that is the city or county or whatnot installs and owns last mile fiber, with connection to one of several competitors for internet service).
Looking at the UK defense industry it does appear that the logical end point for defense procurement would appear to be having one fantastically expensive plane, ship & tank. That would then be too valuable to actually risk using....
One issue really is that there is an apparent lack of valuable, human-doable work to go around because of automation and a highly-connected, globalized world.
Zillions of us are basically working partial shit jobs because either employers don't want to pay benefits or there's no need (low demand/oversupply) for more skilled workers, but the university machine keeps cranking out overqualified people and plunging them into desperation of debt. Many times more entrepreneurs and support thereof are needed to create some decent jobs, because human ingenuity and capability is being left to rot in a fry cooker. (Edit: Investing/mentoring/etc. are hard-to-scale activities except perhaps socially, but they need to happen to utilize more people overall which can be paid more individually and could be where most wealth is created... not as many giant businesses but comfortable cash machines.)