A separate issue is the people who cost $$$$ and never return anything back to society - if they're just lazy or indolent then it's their fault, but if they're disabled or disadvantaged through no fault of their own, helping them is compassionate. An old aphorism is that a society can be judged by how it treats its weakest members.
Exactly, so a strong society is one that would remove its weaker elements from the whole. It doesn't matter if it's their fault or not, especially considering how subjective that is; you could say someone has no work ethic because of the environment they were brought up in, or due to a psychological problem out of their control. No, the proper way to handle people like this is to cut them off completely, and let them find help from other members of society. If they have spent their life only looking out for themselves, and have no one who would help them, that is their own fault.
You've expressed that this is not compassionate, yet I don't remember anyone asking for a compassionate government. I know I don't want Hallmark in charge of government policies. They are obligated to do what is best for the whole of society, not to screw over the hard-working middle class majority for a couple unskilled, inept, disabled welfare bums. Almost all of these people will never contribute anything to society except more children, which will grow up in a scummy environment with their lazy parents and just suck off welfare themselves as adults. This is a disgusting cycle that needs to be stopped, rather than the current system which rewards them with a bonus check for every kid they pop out even though they can't afford food for themselves in the first place.
There are two ways to fix this broken aspect of the government and of society itself. The first is to simply stop all welfare programs, allow people to fend for themselves. The government wouldn't give help to private citizens or large corporations or government officials, or anyone in-between. Those who would die without help will either be motivated to actually do something productive with their lives, or society will be better off. It works out well for the normal people, either way. Perhaps if they let a few people starve to death because they had fifteen kids when they couldn't even manage to feed themselves, the rest of the welfare trash might realize their own sheer stupidity and sub-human way of living, and actually change for the better. This may be considered too extreme though, at least transitioning directly to this from our current society, which is why I offer the second alternative.
The other way they can do it is to increase the downsides of receiving government help. By being eligible to receive welfare, you have to agree to certain terms that are not in your favor. One of them could be that you have to undergo surgery to make it impossible for you to have children in the future. Alternatively, this surgery could just be a requirement if you're on the welfare over a certain time period, or you could be simply forced to get an abortion in the event you become pregnant (you'd always have the option of stopping welfare instead of the abortion). If the woman waits past the first trimester to report her pregnancy because she doesn't want to endanger her checks, then she can either receive the abortion and a hysterectomy, or be permanently cut off from all future welfare.
Perhaps other downsides could even be profitable for the government, which would both reduce the number of people on social welfare and have the program partially paying for itself. If they could make welfare profitable, that would be even better. One obvious option is that to qualify for welfare for any period of time, you have to sign your body over to the government in the event of your death. Then when you eventually die, the government would sell your organs to hospitals, which would generate them revenue. Of course the welfare bums would need to have random drug testing and annual checkups to ensure they aren't abusing their bodies, but that's in their best interests anyways.
I'd say that would be a very insignificant price to pay for all the free money they receive over their lifetime, and at least they would eventually contribute to society in some small way. It'd also stop the welfare trash from being able to use drugs, which if the reason why many of them need to be on welfare in the first place. A lot of people on welfare sell their food stamps for half value in order to get cash for their addiction. It's really quite disgusting, and this would help alleviate that problem as well.
As I've demonstrated here, there are many steps the government could take to simultaneously increase its revenue, decrease its spending, and enrich society as a whole. If the government would take a few of these steps to focus on making the lives of normal people better, and making the life of a welfare bum less desirable, we'd all be much better off.