Economist here. I think you're mixing political science (power distribution + more) with economics (efficient resource allocation + more). Happy to talk more if you're interested.
I have lost count of the times that senior people in your field, have happily admitted how their research is targeted towards the desired outcome of its funding source. Which the people funding the research are fully aware of, they just go economist shopping for whatever result they want to back their policy decisions.
The real issue with current economics isn't that it's not a science, it is that it's not practised scientifically. Those who do look at the field scientifically, have learnt a very great deal from the 2008 debacle - but they're not getting published where anybody is going to read them. But that is far from new. Let me present one of the great, sadly overlooked papers of your field:
David Jones, Emerging problems with the Basel Capital Accord: Regulatory capital arbitrage and related issues
https://www.sciencedirect.com/science/article/pii/S037842669...
Written by a researcher at the Federal Reserve in 2000, he pretty much nailed the causes of the 2008 crash, at least 8 years in advance. His reward was that he got to be part of the cleanup judging by his subsequent career - efficient resource allocation indeed.
https://www.nytimes.com/2017/10/23/opinion/federal-reserve-j...
https://www.nytimes.com/2018/07/02/opinion/trump-trade-war.h...
Another point to be clear about is that economics is not solely concerned with resource allocation. Welfare consequences of policy, counterfactual reasoning, causal inference, algorithmic game theory and mechanism design, etc. are all research areas that are applicable to resource allocation but not only used for such.
Whenever you are negotiating a rate or salary, you are forming a relationship, and the terms of that relationship depend entirely on your relative levels of power and leverage.
I think what you're missing is that money is one type of power, and that basically the study of economics, politics and culture are all just different ways of studying human relationships, of which inequalities of power are a crucial part. There are two broad types of relationships: relationships of rough equality and relationships of gross inequality of power. The latter are almost always abusive, because if you are in a position of much greater power than someone else, it's just too tempting and easy to take advantage of them. Preferences have little to do with it.
Money (or, more commonly, assets) is sometimes included in models, but is not a starting point. If you're looking for models where solely wealth=power as an entry point into the field, I suggest political science (mentioned above) or finance. Overlap with economics in toolkit and occasionally questions, yes, but not composing the entirety of economics.
Consider the question the Obama administration faced in 2009 (and the EU then and later): "Should we inject a large fiscal stimulus, or revert to austerity?"
Very obviously, economic and political issues are inextricably intertwined there.
Your notion that economics is a pure, purely descriptive (and somewhat predictive) "tool", while politics concerns itself with values, is not sustainable.
It's a very adroit slight of hand that benefits the global economic elite: "Hey there, smart professional, I want you to think VERY hard about this problem of how to efficiently allocate resources. Oh but you're not allowed to question why I, the descendant of a colonial robber baron have the ability to personally deploy the wealth of entire nations, and your definition of efficiency is literally just return on investment, no need to worry about questions like 'will the planet remain habitable' or 'is this system in any way just.'"
Neoclassical microeconomics (mostly like what one sees in mid-level undergraduate courses) suggests a minimum wage gives a kink point in individual's budget constraints--implying people may prefer to stay at minimum wage jobs rather than trade time for higher wage jobs, based on preferences. Additionally, if minimum wages rise too high producers will choose to replace labor (people) with capital (machines)--Stigler's argument.
Neoclassical macroeconomics suggests that minimum wage increases may result in inflation (more dollars chasing same number of items), black markets (e.g. hiring illegal immigrants or paying wages under the table), and so on. It is seen as a market distortion.
Labor economics and other sub-fields grant more nuance to these simplistic views. In the simple assessments above, minimum wage policies are at best set up as policies generating economic inefficiencies, at worst painted as immoral policies to support lazy people.
However, we do not live in a neoclassical world. Debates about the economic consequences of minimum wages are still hot topics, decades after they were first engaged, with supporting and detracting evidence. Wikipedia's coverage is a good entry point.[0]
For myself, I tend to come near "Bleeding Heart"/Arizona school libertarian when it comes to social policy--fiscally "conservative" (in that I want to make sure taxes are spent efficiently for the "best" outcomes, which we collectively decide is best), socially liberal, and a foreign dove. The toolkit of analysis emanating from economics does not immediately identify or lend itself to some superior moral framework -- that's on each person to choose themselves. Economics simply helps you identify where waste can occur, whether in the form of bias, inefficient capital deployment, risk, etc. For me, I sleep better at night knowing that my neighbor can afford healthcare and that the janitor I see working tirelessly can put money away for a rainy day.
Some of the more accessible discussions have happened on Barry Ritholtz's blog[1], where one of his contributors defend's Seattle's raising of the minimum wage and resulting impact.
[0] https://en.wikipedia.org/wiki/Minimum_wage#Debate_over_conse...