This is a good idea. It makes simple sense really. Warren Buffet (owner of the very large and successful mutal fund, berkshire hathaway) realised he was paying less % of his income as tax than his secretary, even though he is worth billions. Something like that simply shouldn't happen and the system is obviously not working.
Ideally it should be a gradual curve. Despite having discrete tax brackets, it's not a hard shift from one to the other. It still all actually operates along a curve. As you can see from the image below, even though the brackets have discrete cut-offs, the actual tax rate paid is smooth. Ideally we retain this property.

I think the reason they set a total minimum is more so it cannot be evaded, i.e. you must pay *at least* this much tax no matter what, if you earn over a certain amount.
Of course this goes into the deeper issue of why we tax, who we tax and what we tax. If we could raise tax money via another method, should we still persue this as well?
There are many tax breaks (legal loopholes) used very disproportionately by the wealthy such as negative gearing, capital gains discounts, superannuation taxation, etc. These could alternative be fixed and the need to use the above measure may be eliminated.
At the end of the day, many people will try to evade paying tax or legally minimise their tax. Some argue the best way is just to raise taxes that are very hard to be avoided and do not reduce economic output very much (so called "efficient" taxes). This applies to things like GST and a tax on the value of land you own. You can't really move your land overseas and if you live in Australia you will always need to purchase goods and services. In this way, these taxes are almost impossible for even the richest to avoid.