While I am not a professional or expert in government models, I took a different perspective on the models presented for bureaucracy. Rather than see each of the three as complete and individual models I see the weberian model as being the structure of organization within the bureaucracy where the other two models seem to be characteristics of how bureaucracies function (their incentives, motivators, reasons behind the particular culture of the bureaucracy).
So while our current federal bureaucracies are structured very similar to the weberian model, we often see operations and functions take on characteristics of the monopolistic model. In this we see that without competition there is little incentive for the bureaucracies to become innovative, increasingly efficient, thrifty, and well-managed with a focus on service output. No one is going to compete with most of the agencies in our government like the IRS, EPA, FBI, etc. and therefore we see a lot of waste and lackadaisical work ethic. (This is another reason, if I may interject my personal opinion here, that capitalism makes for such an efficient, innovative, and industrious economy. Incentives and motivators are powerful!)
Furthermore, because there is a weberian structure with monopolism at the highest levels there needs to be some sort of revenue and resource flowing into the bureaucracy. Because of this, I can see how upper levels of bureaucracy often function in the acquisitive model of bureaucracy as they compete for budgeted resources and seek to maintain the monopolistic characteristics the entire bureaucracy has become accustomed to.
I did not truly comply with the question by giving any one type of bureaucracy model to describe ours the best. I think that all three are not only applicable but appropriate. I would give as my final answer that we are structured in America as a Weberian model bureaucracy displaying characteristics and actions that comply with the principles of both monopolistic and acquisitive models.
As for the patronage system of filling bureaucratic jobs I see there could be a few ways in which it would be beneficial in comparison with the current merit system. The patronage system would allow for more efficiency due to the majority party being in control and little resistance from bureaucratic workers. The rules and laws that needed to be implemented with indebtedness to the president for their position along with partisanship would invoke a greater unity among bureaucratic workers. Indebtedness and partisanship are motivators for finding solutions to red tape scenarios.
Furthermore, less qualified workers for positions would guarantee the reliance of many on a few. Management could easily operate and push agendas simply by having greater qualifications or by playing on the ignorance of the staff. Of course this does not speak for the quality of work being pushed through the bureaucracy, but we are only speaking here for possible advantages.
Efficiency and nonresistance would assist the president as he seeks to fulfill campaign promises. Congress’s public approval soars when they “get stuff done” I believe the unity and fulfillment of agendas would reflect well on Congress in the eyes of the public as well.
I realize that The Pendleton Civil Service Reform Act of 1883 and the Hatch Act of 1939 address the issue of patronage within the United States. I would suggest that patronage does still occur on a smaller scale. My father worked for the department of transportation, a state level bureaucratic department, and when he ran into trouble with management from the opposite side of the political spectrum they did very little to assist him or keep him as an employee. An alternate with the same position and different jurisdiction ran into the problems and received full support. The bias was evident and I suspect because the top-level positions are often appointed that there is a trickle-down effect. I wish I had an article to share here or some example more concrete of what I am attempting to explain! In the end, patronage is managed well through these acts but it does not mean that it is obsolete in our structure or that we are truly a merit-based system through and through.
Bureaucracies, American Government 2e, OpenStax, Creative Commons Attribution 4.0 International, 2 ed., 2019, ch.15.