The original sin is more like having your cake and then also eating your neighbour's cake.
The reason that cake ownership and consumption is so begrudged seems to be the judgment of others that boils down to issues of fairness and judgment. Others don't want you to have it all, especially when they don't. The judgment carries through to accusations of selfishness, self-centredness, self indulgence and the rest.
Perhaps there is some of that with some cake consumers, but it seems to me that if you have worked for your cake, planned to eat it, have earned it, paid your school and other fees for it, there can be no reasonable objection to you actually getting to taste it.
The other part of the issue is that there is a principle which is in operation in most societies most of the time: if you don't ask you don't get. So when you are negotiating a deal, your counter-party makes a concession and you ask for another concession, you get accused of wanting both to have your cake and eat it.
Here's my take: never feel shy to ask for both your cake and permission to eat it. Leave to eat it may not always be granted, and you may be judged for it, but so what. At least you tried and sometimes you will actually get to eat it.
You just need to bear in mind that if you intend eating it, there may be a price to pay in extra calories...