Instead of having all of these tax brackets, which for all of the smart people and companies they are meaningless anyway since they take advantage of the hundreds and hundreds of loopholes (also called "deductions") so they don't pay the full amount, why not have a flat 15-20% income tax for everyone instead - rich or poor?

I think it would be simpler, more honest, more transparent, and more fair (slightly favoring the rich, but it more than makes up or it in other ways). You also wouldn't have these endless discussions about whether you should tax the poor 10% (because the tax affects them more) and the rich 30%, or the poor 30% and the rich 10% (because they are the "job creators")?

A moderately fair flat 15% income tax for everyone. No deductions for any special interest.

I'm not a huge fan of subsidies either, but if you really think you need to "make it easier" for some vital or up and coming industries, then you could give them some subsidies for a while. That would also be a more direct and more transparent approach than giving them lower taxes, because then you'd know exactly how much of the taxpayer's money is going into aiding an industry and there would be bigger pressure to end that subsidy eventually.