Do you favor a smaller public sector but oppose austerity because you fail to understand they are the same thing?
Well, they are not. They certainly have a relationship, but no, they are not the same thing.
If, in this context, "austerity" means something other than "reduced government spending" or "size of the public sector" means something other than "total government spending", you should provide whatever (weird) definitions you are using.
there are roughly 700,000 law enforcement personnel in the US and 7 million teachers.
I gave one: 20 seconds of Googling; they are just the first numbers I found. Not a great citation, but the amount of research I'm willing to do in response to your doing none is limited. Now you've done more, and found numbers that say you were wrong by a factor of 3 instead of 10. Well, OK. Personally, I think total spending is a better measure than employees, so this:
http://www.usgovernmentspending.com/year2011_0.html
tells me total spending on Education is more than twice total spending on "Protection", which includes the things you worried were left out and firemen to boot.
Will you concede that these thing indicate some serious issues with law enforcement and education that should be addressed in some way?
I'll concede there are problems that ought to be addresses in both our criminal justice and education systems. Indeed, I have never argued otherwise.
Would you consider any proposals that do not involve spending increases? I won't hold my breath, either.
You won't have to hold it long. Certainly good ideas that will improve things should be done even if they don't cost anything.
Of course, when your economy is deeply depressed due to shortfall of demand, and particularly when monetary policy is exhausted by the zero lower bound, what you desperately need in the short term is for the government to spend more on something. So solutions to societal problems that do involve spending increases would be particularly welcome, especially temporary increases. Personally, I'd go for infrastructure improvement, (because you can do something useful with temporary increases) and an enhanced social safety net (goes away when the economy recovers, automatically comes back next time). Education wouldn't be temporary, but, in my opinion, good solutions are likely to involve spending increases (the other countries that you point out we are doing worse than tend to spend more). I wouldn't go for criminal justice because I don't think the things that are wrong there need spending to fix.
But frankly, if I wanted to have a serious public policy discussion, I wouldn't pick someone who uses North Korea as an example of what a larger public sector would look like, or who says "low wage jobs are plentiful" about today's economy. Sometimes I just take guilty pleasure in pointing out that other people are saying something inane. But I've got my fix now, so I think we're done. Next time, if you want people to take your ideas seriously, don't start off by saying something stupid. By the time you get to "What I actually meant was this totally different thing."... nobody cares. HTH.