If you remove taxes on a product then a product can sell for cheaper. US tends to tack on sales tax after the purchase, this isn't common to the rest of the world, where taxes are part of the price.
The mere existence of sales taxes tends to be part of the price of goods and services in the USA - even for products such as food that are officially 'not taxed' in many jurisdictions.
The price inflation caused by government is just hidden. People don't see it so they don't realize it's there (mostly because they don't understand how businesses and the economy work and the real cost of goods and services).
Relatively few businesses sell only tax-exempt goods or only provide tax-exempt services.
As such, for the majority of businesses that sell to consumers, there is some overhead associated with making sure the business complies with the tax rules for the goods that are taxed, and can prove it through an audit.
Sales tax rules are notorious for being incredibly obtuse - and they change frequently. If you talk to small business people, you find almost all of them hate sales taxes with a passion because they are such a pain to deal with.
A lot of the rules require human interpretation. In some cases, you can talk to three different government officials about a tax question and get three different answers about whether or not tax is owed and how much.
As a result, the business response to sales tax policy can't be completely automated with a computer program - and even for those businesses where a computer program is practical, some human being has to interpret the rules, usually with an accountant and a lawyer, so the program can be updated every time the tax rules change. Accountants, lawyers, computer programmers - these people don't come cheap.
The overhead associated with sales taxes is significant, and it becomes part of the cost of doing business.
Those costs have to be paid for by income from the sale of goods and services, so typically they are spread over all the goods and services sold by a business, whether or not the individual good or service is taxed.
Thus, sales tax policy increases the prices of goods and services, even those not directly taxed, through creating a hidden tax.
This is one of the reasons why the decision in Wayfair vs. S. Dakota is going to create big problems in the long term *. But I digress.
Since almost every business has to deal with sales taxes, the whole supply/demand curve tends to shift - and you get higher prices as a result - in other words, in most markets nobody can compete against each other to lower the price increase forced by sales tax overhead, so everybody has to raise prices.
As a secondary effect, small business suffers, since the burden of sales taxes is higher for a small business than a large one. This has all sort of negative economic implications, but certainly some of them are overall higher prices on average as a result of less competition, fewer employment options and less bargaining power for workers, lower product quality, and so forth.
A healthy small business sector does a lot of good things for an economy - and the absence of a healthy small business sector does lot of bad things that hurt everybody economically, but the poor and the middle class bear most of the burden.
So, in general, you have two different effects flowing from the existence of sales taxes that have the effect of raising prices. None of this money from the price increase goes to the businesses - so it's effectively a hidden tax created by government policy.
The present situation - where the price of a good is being lowered to reflect a lowered tax by the actual amount of the tax - is actually quite usual. Many businesses are doing a lot of things right now to bolster their reputations - and that's a good thing.
There are lots of hidden taxes that work like sales tax does. Some estimates place government policy variables as being responsible for 64-73% of the cost of living differences in US states [Schlomach, 2017]. It's likely that government policy variables are also responsible for an similarly large portion of the cost of living differences from year to year (otherwise known as inflation).
The present situation - where we actually DO have too many dollars chasing too few goods - is actually pretty unusual - and the primary cause of inflation in normal circumstances is likely to be consequences (unforeseen or otherwise) of government policy decisions.
All these hidden taxes created by government policy are HIGHLY regressive, and a big part of the reason why the proportion of wealth going to the 1% is increasing in the USA. A lot of these policies involve something economists refer to as 'rent-seeking', which basically means manipulating the government and legal system to increase one's income at the expense of society as a whole.
For more information on this problem, you can look at The Captured Economy: How the Powerful Enrich Themselves, Slow Down Growth, and Increase Inequality - by Brink Lindsey and Steven M. Teles [Oxford University Press, 2017].
The type of sales taxes used in most other developed nations (VAT taxes) are actually MORE harmful than US sales taxes, because they are applied at every step, - and they come with every bit as much overhead if not more - so the final price ends up being a lot higher for equivalent goods as a result of compounding through the economy (each business has to pass it's costs on to the next until you finally get to the consumer). This is largely offset in these nations by strong social policies that return a lot of that money to ordinary people through policies such as health care.
But it's not an accident that the Scandinavian nations have higher household debt rates than the USA. Rather, the high household debt rates are a result of the bad tax policies and the high proportion of regressive taxes such as the VAT. Given that a large proportion of US debt is at least in part likely to be associated with medical expenses, and given that the USA does a particularly bad job of regulating banks and credit card companies, resulting in artificially high debt levels, the high household debt rates in Scandinavia are particularly telling.
The rich make up a tiny portion of overall consumer spending. As such, sales tax policy is essentially a tax break for the rich, carefully disguised as something people can somehow 'avoid' if they are frugal. They just don't tell people that they're getting screwed through the hidden tax aspect of sales taxes - and that even the most frugal person can not avoid paying higher prices because of the existence of the sales tax. The cheap inner demon present in most people doesn't carefully scrutinize the real costs of things.
Total consumer and business spending in the USA completely dwarfs the income of governments from progressive income taxes, so even a relatively small impact on consumer and business spending through hidden taxes and tax-equivalent policy means that the poor and the middle class bear most of the burden of government.
Sales tax policy is inherently regressive: a progressive income tax is a far superior solution to the problem of funding government.
* Aside from having extremely serious negative legal ethics implications - what kind of insanity led them to think that requiring every business to know the sales tax laws in every legal jurisdiction where a customer might reside was going to be a good thing for anybody but the lawyers, or how such a policy could possibly be justified given that the 9th Amendment certainly protects the right to ethical practice of law? Even the appearance of conflict of interest must be avoided when reasonable alternatives exist - and they certainly do here ...