Is it considered acceptable or unacceptable to use currency as a measure of utility?

There will always exist at least one economist who condones measuring utility in US dollars and another who does not. However, I am wondering which way the majority of contemporary economists lean.

Would it be safe to say that at least 75% of author of academic papers published between the years 2000 and 2020 measured utility in terms of US dollars? Is it standard practice, or not standard practice?

I took many economic courses in college, but I have no idea what is done in contemporary economics research.

One potential drawback to approximating utility with currency is that currency is associated with diminishing marginal utility per unit of currency.

Suppose that Bob is stranded in the desert with two bottles of water.
Sarah is stranded in a similar desert with six bottles of water.
If all other contributing factors are the same, then it hurts Bob more to lose one bottle of water than it hurts Sarah to lose one bottle of water.

If someone who made 10,000 USD last year earns 9,000 USD this year, their decrease in personal happiness (utility) might be greater than if someone who made 101,000 USD last year year earns 100,000 USD this year.

Statistically speaking, in the United States, wealthy parents tend to spend more hours playing with their children than poor parents. I once read an economics textbook where the author expressed incredulity as to why that might be.

If you make 300 USD per hour as an attorney at law, the opportunity cost of spending 4 hours with your kid(s) is 1,200 USD.

If a poor person spends the same amount of time with their children, then the opportunity cost might be \$40 in forgone wages.

The opportunity cost, in US currency, of a wealthy parent spending time with their children is greater for the wealthy parent than for a poor parent. The author of the textbook went as far as to deem the phenomenon "a paradox."

The solution is simple to me: The poor person would lose more utility, yet less money. The wealthy person would give up a great deal of money, but very little utility, to play with their children for 4 hours.

If a wealthy attorney plays with their kids one more day per week on average, then the family might own 3 cars instead of 4. However, if the poor American parent plays with their kids one more day per week on average, then family might forgo new shoes for the children and the family might eat soup made from water and stolen ketchup packets every Friday. Having 3 cars instead of 4 cars hurts less, relatively speaking, than having uncomfortable shoes and eating badly. The poor person stands to lose quite a lot of utility when small financial losses occur. The wealthy individual loses very little utility when small financial losses occur.

Is currency is a poor quality measure of utility/happiness?

Now in many situations, one can use so-called "money metric utility functions." Start by holding prices fixed (this should already tell you a fundamental limitation of the idea.) For each commodity bundle $$x$$, let $$u(x)$$ be the price of the cheapest commodity bundle at least as good as $$x$$ according to the preferences. Under some assumptions, this gives you a genuine utility function $$u$$ representing preferences and it gives you actual dollar values. But the natural interpretation depends crucially on prices being fixed.
If you assume that agents' utility functions over pairs $$(x,t)$$ of consumption bundles $$x$$ and monetary transfers $$t$$ are quasilinear in money, $$u_i(x,t)=v_i(x)+t$$, then $$v_i(x)$$ measures $$i$$'s WTP for $$x$$. In a utilitarian framework the sum of utilities is then a social welfare function satisfying Arrow's axioms (apart from universal domain of course) and measuring welfare in monetary terms. Introductory Microeconomics textbooks do that tacitly when calculating consumer surplus as the "area between the price level and the demand curve" and summing up consumer surplus and producer surplus to get total welfare. However, the quasilinearity assumption implies that there are no income effects, which is quite unrealistic.