If the government wants a tax to be paid they need to make it simple and unconditional. If there are loopholes or ways to legally avoid it, they will be discovered and people will take advantage of them.
In a good and just society there is a large overlap between them, and in others there is less overlap.
But it's impossible to build a legal system where there is a 100% overlap, and it would most likely be a broken society in other ways.
I totally agree with your second paragraph, that the government needs to remove loopholes and other ways for people to weasel out of contributing to society. But there will always be some corruption and a lot of money to be earned by only taking from our shared resources and never contributing back.
I strongly disagree with this one. It's not that hard to not define loopholes and exceptions. Really, a simplified tax system without such should be the goal, and then the circles so match.
Yes, it should be, because in addition to complex tax systems introducing loopholes and exceptions, they also become more complex to collect.
If taxes were simple and straightforward, you would sink an entire industry in the US. There's a whole money pit around just getting money from people to their government. That's money you could, instead, be getting as taxes.