There are some aspects of Denmark's system re: your last point that I think other European countries could benefit from. However, it's still quite poor when it comes to providing a way for starting a business to be recognized as an alternative exit from unemployment.
The good parts are a general vibe that the unemployment system is less about welfare, and more about matchmaking. One structural help is that it's run quasi-independently by several non-governmental (though state-subsidized) organizations. Each of these organizations, an "a-kasse", focuses on different areas. For example, I'm a member of one that focuses on researchers. This means they can provide more specific advice to my situation, and also means they develop relationships with both sides of the unemployment puzzle: companies in relevant areas will come to them looking for talent, and the a-kasse will try to connect unemployed people with seeking companies. So they see themselves not only as an unemployment agency, but also as a recruiter to some extent. If you can't find a researcher specializing in data mining, for example, you might go to the researcher "a-kasse" and ask them if they can hook you up with one. This also makes the a-kasse much more informed about what the job market in their area looks like, which in turn guides their educational programs.
Initially it's fairly self-serve, with an assumption of good faith that you're just temporarily unemployed and doing your best to fix the problem; there are offices where you can get assistance, or you can get it online, with things like resumes or job listings. Then, if you're still unemployed after some time, it becomes more mandatory, where you have to go in regularly, so they can try to debug why you're still unemployed, and what could be done to fix the problem. That might include assistance finding/applying for jobs, taking training courses, or other things.
Past that, if the problem is lack of demonstrable skills or work experience, there's a quasi-paid internship program: a company will "hire" you for 3-6 months, but you remain on unemployment, so are almost free to the company, but they do have to pay your pension contribution (this gives the intern a modest financial benefit, but mostly serves to make sure the company takes it at least a little seriously, since the intern isn't 100% free). The hope is that that will turn into a regular job, or at least gain you enough skills/experience to get a similar job elsewhere.
If all that fails, after some years, then it becomes more like a regular welfare system, but this up-to-2-years "a-kasse" system is much more geared towards assistance/adaptation/upskilling.
There are indications that is where UK system is trying to go, but there is a huge weight of baggage - everything from pointless stories about 14 children families living in million pound mansions and sponging off the state to reluctance to deal with structural geographic issues (frankly if you are under 25 move to London to get a job, there is nothing anywhere else for a certain value of nothing)
The good parts are a general vibe that the unemployment system is less about welfare, and more about matchmaking. One structural help is that it's run quasi-independently by several non-governmental (though state-subsidized) organizations. Each of these organizations, an "a-kasse", focuses on different areas. For example, I'm a member of one that focuses on researchers. This means they can provide more specific advice to my situation, and also means they develop relationships with both sides of the unemployment puzzle: companies in relevant areas will come to them looking for talent, and the a-kasse will try to connect unemployed people with seeking companies. So they see themselves not only as an unemployment agency, but also as a recruiter to some extent. If you can't find a researcher specializing in data mining, for example, you might go to the researcher "a-kasse" and ask them if they can hook you up with one. This also makes the a-kasse much more informed about what the job market in their area looks like, which in turn guides their educational programs.
Initially it's fairly self-serve, with an assumption of good faith that you're just temporarily unemployed and doing your best to fix the problem; there are offices where you can get assistance, or you can get it online, with things like resumes or job listings. Then, if you're still unemployed after some time, it becomes more mandatory, where you have to go in regularly, so they can try to debug why you're still unemployed, and what could be done to fix the problem. That might include assistance finding/applying for jobs, taking training courses, or other things.
Past that, if the problem is lack of demonstrable skills or work experience, there's a quasi-paid internship program: a company will "hire" you for 3-6 months, but you remain on unemployment, so are almost free to the company, but they do have to pay your pension contribution (this gives the intern a modest financial benefit, but mostly serves to make sure the company takes it at least a little seriously, since the intern isn't 100% free). The hope is that that will turn into a regular job, or at least gain you enough skills/experience to get a similar job elsewhere.
If all that fails, after some years, then it becomes more like a regular welfare system, but this up-to-2-years "a-kasse" system is much more geared towards assistance/adaptation/upskilling.