I think the problem with our western democracies is too many voters want their cake and eating it at the same time. If we do like some nordic countries make tax returns public documents, half of the problems will disappear. When rich people have to pay their fair shares of taxes, they won't need to buy up politicians.
Who buys politicians? If you mean political contributions, all parties are funded that way. I heard (I think) that Labour got 2.5 million handed in this week. The Cons got about 100k.
As for proper bribes - well I have not seen any evidence of that.
The tax code is ENTIRELY in the hands of governments - and governments of all colours have made rules which are there for people to follow. They range from establishing tax rates at different income levels, setting the level of tax on companies and dividends and setting VAT, or fuel duty and everything else including whether foreign residents pay tax on foreign income (non dom).
If business men and companies act fraudulently, by hiding income - then they break the law. If a small trader puts a lot of cash in his back pocket and doesn't put it through the books, he commits a crime. Prosecute them and make them pay massive penalties.
As for people who correctly use the tax allowances they are allowed BY LAW in the tax code. There is nothing wrong with that. The rules were made by a succession chancellors to encourage and facilitate business and wealth production.
Some of us are old enough to have been adults when Denis Healey a Labour chancellor was boasting about squeezing the rich until the pips squeaked. The rich just left the country and the tax take fell. When Thatcher (who did some good things and some bad things) cut the top rate of tax from about 95% to 40%, the tax take rose considerably. I think it is quite likely, that abolishing the non-dom rules will simply cause super wealthy people, like Mrs Sunac to leave. All the VAT they paid on their frequent expensive purchases, will go with them. So what will be gained? Likely - nothing.