Imagine you have a barn with mice and you get a cat to eat the mice. Most of the mice run away. If you measure only how many mice the cat eats per day, you might be underwhelmed, and might think the investment in the cat was not worth it. But you should care less about the cat's diet and more about the fact that there are fewer mice.
Isn't this the theory behind mandatory minimum sentences etc. in the War on Drugs? It doesn't seem to work.
And it's also misunderstanding where most of the problem is. It's not that so many people are committing tax fraud. They recovered a billion dollars? The federal budget is over 6 trillion dollars.
International corporations avoid taxes by structuring their activities in ways that minimize taxes. It's legal. The problem is the structure of the tax code, which tries to tax "profit" instead of sales or wages or something else that physically exists in a specific jurisdiction, and then the "profit" ends up in whatever country has the lowest taxes.
Over the last 100+ years, slowly, primary taxation has shifted from corporations and resources to individuals. One can see why this makes sense, as policy with respect to trade has shifted as well. We've become more global, as eluded to, and the least up to this century the goal has been on "reducing trade barriers". So tax has shifted to "consumption tax" (gas tax, sales tax, sin tax), and personal income tax, as it is harder for people to be in multiple tax jurisdictions.
At least, this is how I see it. Your citizens live here, own property (your municipality gets income), have to eat/do things locally (consumption tax), and can't claim they live elsewhere easily, for the "average Joe" is just going to have a simple tax structure, and it's known where he hangs his hat.
Corporations are just a legal fiction around some economic activity. If you're even tangentially involved in that activity, some of the money will end up coming from you. But since people don't want to hear that, the policy that passes is the one that obfuscates what's really happening enough that people can no longer understand what's really happening, and everyone who likes the status quo can point the finger at someone else and claim they're the villain.
Probably the best thing we could do in the US is take a bulldozer to the entire tax code and constellation of existing federal programs and replace them with something much simpler, like VAT as the only federal tax and made progressive through a UBI. No more tax avoidance, shell games, poverty traps, lobbyist corruption through the revolving door, massive federal bureaucracy, just the most basic system that causes lower income people to pay low or negative effective tax rates and higher income people to pay higher effective tax rates.