I can answer the question of how to improve it. If you receive any types of federal benefits you must show active participation in looking for work, you must attend any workshops or job fairs put on by your state's job commission. You must make every attempt to better your situation. There needs to be repercussions for not following the rules. If you need government assistance past five years because you are not making any attempt to improve your life you lose your benefits. If that means you can no longer feed your children then your children become the custody of the state where they will at least be taken care of.
Emotively, I can see the logic. Don't give money to lazy f**kers that don't want to work.
In practice?
I genuinely believe people are driven by a desire for survival -> economic security -> status -> self fulfillment, in approximately that order. Poor people, or those perceived as lazy are no different - it's only when you can't see a path to the next tier that you'd lose motivation and sit where you are.
If we accept that survival is easy to meet, and largely being met in America today, a lot of the poorest are at the point of surviving, but lacking security.
Example: I have a choice between welfare or working in an Amazon warehouse, which I think helps illustrate the predicament that most people at the level of manual jobs face. That warehouse has virtually no chance of career progression. Status? Zilch. Security? It pays just enough to survive - so no more than being on welfare, arguably worse as I have to spend 8 hours working hard. Saving for a better future is an impossibility.
In order to be motivated, I need to see a path to the next tier. These sorts of jobs don't provide it.
Get educated and find a better job you say. Yes, let's fund education properly. But let's also acknowledge that learning gets more difficult as you get older. It's a solution for the young (assuming they have economically-secure parents that can support their lives while they study) less so the old.
So I'd ask, what would harsh welfare rules achieve?
Well, given the intrinsic motivations of humans, one would probably stay on welfare until the time limit was up, then go work for Amazon or Uber. Now, Uberzon benefits from the labour, but the situation of our worker is just as precarious and their lifestyle is worse. What's more, they no longer have time to look after children or further themselves in any way, so it's possible the state would have to step in in other areas, like childcare, like taking them in to the custody of the state. Which, by the way, is enormously expensive!
Taking a child into the custody of the state would be no cheaper than paying benefits to their parents. In fact, parents are always going to be the cheapest way to care for children - they normally do it for free. Once you factor in all the court hearings, custody battles, abuse scandals, and emotional damage to children resulting in worse outcomes for them as adults, I'd expect this policy to be orders of magnitude worse in the long run than just paying benefits. Far from reducing inequality, this would entrench it for generation after generation.
I guess what I'd say is, what if you grew up in that situation? What would you do? If you think harsh rules would improve the outcome for you and society at large, fair play, but I don't think it would for me or anyone I know. It's not just the worker, but their family that needs to be considered, and the long term impacts, not just the short.