I don't think it is irrelevant to the discussion. When we tax about nation tax policy and what type of taxes should on citizens, it is important to remember that we are a representative democrasy where the voice and opinion of the citizen is highly important and plays a crucial role in policy and legislation. As such, anything which impacts or helps from that citizens opinion is relevant - at least to the citizen. To adopt the restrictive rules of an academic debate and pretend that there is only one type of risk - FINANCIAL RISK - that is important is going to give us a false picture of the citizens concerns.
Then by that logic, a person who is in a high risk job should be taxed less? Somehow I believe you answer would be no by your other comments. If your point is that regardless of the source of money the tax should be the same, then what point does the physical risks of the job hold to how the income from it should be taxed. When it comes to the issue of taxes and finances then yes financial risk is a legitimate factor and physical risk is not. On the other hand, when it comes to matters of compensation of labor/service given, then yes the physical risk is a factor that comes into play. Logic still comes into play and unless you can determine a logical reason why physical risk should be a factor in taxation vice compensation then please present it. Taxation and compensation, while both fruits (i.e. financial in nature) nonetheless they are apples and oranges.
As to your compensation argument, whle the pay holds true, many people have lost their retirement pensions - and many more feel they are at risk - so that point still remains valid.
Again moving the goalpost, albeit not as far this time. One is not required to participate in a company pension plan, and personally, anyone who does is a fool. Regardless, short of placing that money under a mattress any retirement savings that are invested somewhere is at risk. But those are AFTER PAY dollars, regardless of whether or not they are pre-tax or post-tax (401k vs Roth IRA). In otherwords, whether or not that money is invested, it is still earned and thus the risk to the individual is taken seperate from the job itself. You still get the same amount of money for 40hr/wk, 52wk/yr over 20 years, whether or not you invest that money and regardless of what you invest that in. Therefore there is still no financial risk in wage/salary income.
My assertion is that a million dollars coming in to ones pocketbook or account still a million dollars regardless if it is in wages, lottery winnings, capital gains or inheritance. It looks the same and it spends the same. We know darn well that the wealthy dispropiortionately benefit from both the laws on capital gains and inheritance while the average worker does not reap these benefits to the extent.
While it may seem so to you, it simply isn't so, or at least to this citizen's view, and obviously my voice and opinion is as highly impoertant and as crucial as your own. Inheritance is a straight up no risk, no work form of income. Lottery winnings are no work, small risk income assuming any winning is done. Investing/capitol gains is high risk, and as to work, well it depends on what you are going to consider work. A lot of investigation usually goes into determining if an investment has a chance of producing a yield. It's a full time job for some people. So I would not call it a low work or no work kind of income, but the sad reality is that some people do invest with little to no work and usually lose everything doing so. Finally, wage/salary is a no risk, high work form of income.
Now should they be treated differently or the same? That is a legitimate question and one to be discussed. But it is a faulty premise to call them the same and it is not against logic to consider that since they are different they can be treated or taxed differently.