It is incredibly hard to understand what people are doing, and how that works out in a complex organization!
The effort and likelihood of reasonable success is a precondition for your argument.
I have been in a lot of companies, and I have seen soooo much useless busy work. Including my own well-paid IT consultant job, not infrequently.
Employees and managers on all levels try very hard to justify their existence. When they are under-employed they may also start looking for new projects themselves, which the next level of management is okay with because it appears that they are doing something useful, and they don't have to deal with that problem.
Overall, I will claim that your argument is far too simplistic and ignores the complexity of humans and their organizations.
Its not though, its the same layers of documentation, paperwork, upper management approvals, legal and HR approvals. The only exception being blatant policy violations like drug use, etc. where immediate dismissal can be done.
If you are talking about mass layoffs, for large corporations they still have to file paperwork for the WARN act, look at laws in various states around employment, get legal, HR, etc. involved.
I've seen both mass layoff and single individual layoff first hand and the only thing that might be different with Federal employees is a union. And in that case a union operates mostly the same if its serving a large corp or a government entity.
Private sector entities can have less “dead wood” because it is easier to get rid of people, and because there is a stronger incentive to do so - reducing salary/wage expenditure increases profit. Yes there will always be some in both, but having worked in both public and private sectors, you see more of it in the public sector.
A few days ago I was talking to the employees of a homelessness charity at a social event, one of whom was telling me he felt NGOs waste money more than for-profit businesses, but not as much as the public sector. The reason he said it, was his employer was still paying rent on an office building despite it being uninhabitable due to mould and water damage - my question was if the building was uninhabitable why not cancel the lease, surely that would give justifiable grounds to do so, and then they’d have more money to spend on the homeless (or, he added, pay their employees more)