I do, I sometimes don't claim back charitable donations. I don't claim depreciation on my rental property I do not think it is valid expense. I claim deductions that I believe to be fair and for business purposes, I do not claim ones i don't, legal or not.
But the real reason is probably everybody could get away with paying less tax if they knew what they where doing. The reason normal people don't is it is not feasible for the average person to pay millions to an accountancy firm to set up tax shelters. Once a company starts making billions however those admin costs become insignificant.
Why couldn't you set up a company in Ireland and contract out of that instead of being directly employed by your company. (they would think you where dodgy but only because it isn't common practice). Your employer is paying you the same amount, what difference does it make to them. The hassle is just not worth it, at least for the common man.
The problem is that you don't have stockholders that will sue you PERSONALLY if you pay more taxes than you have to. Public corporation executives can be personally liable for intentionally harming the financial standing of the companies they run.