The flaw is that you can't be sure if the money you are paying as tax is actually ending up with the poor.
For all other charity institutions, one cannot be sure either whether they bring the zakat at the rightful place. In the end it's a matter of trust. As for your other arguments:
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Social welfare payments are not always means tested. A middle-class person living comfortably off savings can claim social welfare payments after being unemployed for long enough in a social welfare state.
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It's not as easy as it sounds. In order for you to receive money due to unemployment due to illness, you have to have had a medical check-up with a medical written report indicating that you are 100% unable to work. Only in that instance will you get money. If you are only 50% unable, you get halve. So here indeed my taxes will be only going to those that are in real need of money.
If you are unemployed due to other circumstances, you have to provide evidence each month that you applied for jobs that fit your qualification. Besides, if you are unemployed for less than a year you don't get anything at all from this institution.
Moreover, suppose you are living off savings, you cannot claim additional social welfare payments if your savings provide you an income which is higher than the minumum salary. If your savings are lower than that, social welfare will only give something additional to bring you upto the minimum salary level. So here too, my tax money indeed is a form of allowance for the needy. Furthermore, if your income based on savings is larger than the minimum salary you have to start paying these taxes too!
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Pension tax is similarly paid to all, irrespective of whether they are poor or not. When I retire, I fully intend to benefit both from my private pension (which should inshallah be cozy by that time) as well as taking pension paid for by the taxpayers. I will inshallah not qualify for zakaat but will claim tax-funded pension
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Here I agree that all pensioners will get something from welfare. However, if you don't have any additional pension savings, you get more from social welfare than someone who gets a lot already from private pension funding. Also, widow(er)s who don't have any other means of income, get welfare from here.
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In most social welfare states, the right to claim medical aid is not completely means-tested either. A wealthy person can choose to receive your money if they don't want to use their private insurance.
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This is not the case here. Everyone by law is forced to have medical insurance for the basic medical needs. The medical social welfare I'm talking about are those persons who are so poor they cannot even afford that. Or persons who have such chronic and costly illnesses (such as mentally retarded persons, severely disabled or injured people) that they will never be able to pay all the costs themselves. So here too, my tax money will only go to those who really need it and would never be able to get the medical care otherwise
Dentist payments fall under a totally different category here (which is compulsory insurance as well btw, but is not included in the 6% above).