You're confusing the symptom and the reason.

The symptom is that emergent cases are getting worse care.

The reason is that non-emergent cases go to the ER even when it is known apriori the case is non-emergent.

The solution is to disincentive non-emergent cases from going to the ER when it is known apriori they are non-emergent.

How you actually accomplish that could be violence (use IRS men with guns to fund PCPs by taking away money from someone else they could have used on necessities as we currently do in social security), it could be charity (monetary or labor donations for medical services), or it could be finding ways to make people pay for abusing the ER system, or it could be deregulating health care so it's cheaper. There are lots of ways to implement the solution but your comment presents a false premise it's the only choice.

Your reason here is the exact same as mine. Non-emergency cases go to the ER because they have nowhere else to go to deal with their needs.

Your symptom is mostly just a rephrasing of my same symptom. ERs are flooded and have worse outcomes overall because of the crowding of non-emergency cases.

So no, I don't think I'm confusing anything.

And in the end, sure. I only gave one potential solution to "give them somewhere else to go", but in the end the solution is still to have them go somewhere else regardless of how we accomplish that. I personally think providing "free" primary care is one of the better ones. Seems like the charity route isn't working out well enough. You're not going to get people with nearly no money to "pay for abusing the ER system" unless you're talking about jailing people (rats according to you) just trying to access the only point of healthcare they have access to. While you might make some healthcare a bit cheaper with deregulation you'll probably still have crowds of people unable to afford it and you might also end up with a lot of other worse outcomes depending on the regulations you cut. Looking around the globe, it seems like funding primary care for all usually leads to the best outcome for society overall and would do a ton to reduce the reason we both agree leads to bad outcomes in ERs.

We're already paying for their primary care, we're just paying for it in the least efficient manner. Its not really new money we'll have to find. Far cheaper for them to just stroll into a regular clinic and get these services than have them use up precious and expensive ER resources.