There are several problems with your proposal, and there are several claims that you make that are actually not correct.
First, consumption taxes do not directly combat inflation they actually typically directly result in at least temporary inflation. Inflation is increase in price level. When consumption taxes increase, empirically (e.g. see Carare, A., & Danninger, S. 2008 or Benedek et al. 2015), price level increases since at least some of that tax increase is passed onto a consumer. The evidence comes from regular consumption taxes, such as GST or VAT but there is no economic reason why some sort of individualized progressive consumption tax would not have the same effect, in standard micro supply-demand models the consumption tax will increase prices if it is binding, excluding some people might lead to smaller effect overall but then you will also get smaller effect on demand. Consumption taxes affect demand precisely because they increase prices consumers face, whether explicitly or implicitly.
Now this is just a temporary 'short-run' effect because they result in shift in level of prices (inflation is ongoing process), but it is still effect that makes inflation worse in short run. The consumption tax can have also simultaneous downward effect on inflation, but this effect would come from the negative effect of consumption tax on aggregate demand, which hurts the economy and increases unemployment rate, so this is the same harmful effect you tried to avoid.
In addition, if government spends the money collected by the tax then it will offset large portion of the negative shock to aggregate demand. Most governments spend more money then they collect in taxes so it is very unrealistic to imagine that the same governments will exercise restraint in spending extra tax revenue from such tax.
Moreover, the consumption 'brackets' you propose are not new proposal but are generally unworkable. Government does not have information on your personal consumption. In order to collect this information government would have to collect your personal information every time you enter a store and purchase something. That might be trivial when using credit card, but it becomes extremely cumbersome with cash. In some countries people do not even have ID. Even if you would institute some bureaucracy that would collect information on people who make cash transactions, such tax could be trivially avoided by asking friends or other third parties to make purchases for you. Hence such tax would be easily avoidable, only solution to this problem is either complete abolition of cash and removal of any privacy when it comes to purchases, or having uniform consumption tax rates (hence why countries have GST or VAT).
Furthermore, this is bit beyond this question but from long-run perspective income is equal to consumption, as saving is just postponed consumption, so any sort of redistributive measure (otherwise I see no point in consumption brackets) can be simply always implemented by taxes and transfers on income side where data collection is infinitely more easier compared to consumption and hence such differentiated consumption tax is pointless.
Second, inflation is actually caused, among other reasons, by low interest rates (e.g. see Alvarez et al 2001). Hence, if you keep interest rates low you are fueling higher inflation. You are not really addressing (one of the) root cause(s) here if you want to keep interest rates down.
Third there is very little evidence that low interest rates promote sustainable economic growth. In fact in most economic models of growth there is no nominal interest rate.
Moreover, you claim that higher savings have negative effect on economic growth but that is not true. Growth is actually positively related to savings rate in poor countries, although less so in richer countries that are already on technological frontier, but it does not have negative effect on economic growth Aghion et al 2016). Furthermore, both saving and investment decisions are determined by real interest rate not nominal interest rate.
Nominal interest rate allows people borrow more new money but it does not change the real amount of resources or stuff that is out there. Lower nominal interest rate can stimulate economy when it works below its potential, because that implies there are some underutilized resources people are not tapping to just because of some nominal constraints. However, inflation is clear sign that economy is operating above its potential. At such point low nominal interest rate cannot affect economic output it can only generate more and more inflation. This is why lowering interest rate is used to combat recession, but country can't just grow by lowering its interest rate, if that would be possible there would be no poor countries.
