Maybe don't generalize from a few personal anecdotes to the functioning of the entire 4 million employee federal government?
But to directly answer your question: if you want your dollars spent effectively, you should care about fraud rates in services you pay for (public or private).
https://www.cfo.com/risk-compliance/2021/03/ubiome-founders-...
The US government spends about as much per capita on healthcare as say France, but doesn't cover everybody and without part B is pretty incomplete.
See this plan for example: https://en.m.wikipedia.org/wiki/Healthy_Americans_Act
It would transition away from employer-provided health insurance, to employer-subsidized insurance, having instead individuals choose their health care plan from state-approved private insurers. It sought to make the cost of health insurance more transparent to consumers, with the expectation being that this would increase market pressures to drive health insurance costs down.
Health insurance is one of the least concerning things for the government to get involved in with healthcare, really. Worst thing that happens is they don't insure you or the procedure, and you have to pay for it yourself somehow.
I would question the viability of government for handling many things, but collecting taxes and distributing funds is one of the things they usually are pretty good at. Some of the leanest health insurers in the US in terms of overhead are public enterprises, e.g. the VA and various state assistance programs.
It's a very similar system, the real difference is that it's illegal to not have insurance, so you are "forced" to always be insured, and unemployment support is more generous.
This sounds more like a hypothecated tax.
American government is a uniquely incompetent form of government. Despite being one of the largest & most expensive governments it gets little to nothing done. Anything that is 'done' is often done far over the original projected budget.
Objectively untrue by any serious metric you'd like to go for, and in particular government-run health insurance programs (Medicare chief among them, but also the VA) are notably well-run and have low incidence of fraud while maintaining remarkably low overhead.
And yes, SS is absolutely welfare and it is extremely effective. It reduces the poverty rate of the elderly by nearly 30%. It also reduces, directly and indirectly, child and young adult poverty by meaningful amounts as well, 1.5% and 3% respectively.
Regarding your first point, I disagree. I think the intention is clearly to provide a direct benefit, but that isn’t always the effect. One example which seems to be entering the zeitgeist now is student aid. The presence of additional student aid has a high correlation with the rise in tuition over time, but I think we’d all struggle to say it was commensurate with to the cost.
Addressing your second point re: social security and perhaps generalizing my first point slightly, I think the statistics you cite are reductions in poverty vs simply abolishing the benefit. I don’t think they measure the counterfactual scenario of there never having been social security to begin with, and those current seniors having had their take home pay increase by some portion of the 15% of their gross pay which otherwise went to SS. Additionally, it doesn’t take into account the future debt servicing cost of current SS recipients on future generations.
SS also has always been a Pay Go system and doesn't have any debt servicing, actually the reverse is true, SS is owed money from the US government. That is, SS lent the US government money. That government debt would exist with or without SS as federal government spending is not constrained in any way by tax receipts, so SS's impact here is moot.
To your point about student aid, that is far more complicated. While it is likely true that the existence of the aid has resulted in some upward pressure on tuition, it is not the only factor. Increased demand both in quantity and quality of services, reduction in direct public aid to institutions, and increasing administrative costs among other things all play a part. Without student aid, it is likely true that prices would be lower, but probably not nearly as much as one would assume, and we would have a far less educated populace. The latter being a substantial negative in a world where the best paying work is and continues to be more knowledge based.
Also, education is rather interesting special case in that it's a highly price-insensitive good in the modern economy.