In the countries that I am familiar with (such as Canada), using barter to avoid taxes is definitely illegal. You are required to report the dollar value of the exchange as revenue. It is treated as an implicit trade of cash along with the trade of goods. Since I am not going to give tax advice to random strangers on the internet, please consult the tax laws of your jurisdiction.
Canada Revenue Agency guidance on barter: link to CRA page
There are exemptions, such as for little kids trading cards on the playground. The idea is that you cannot be earning a livelihood.
The authorities can detect this activity the same ways that they can detect people working for cash. It’s not easy, but it can be done. They can have undercover agents, get tips from whistleblowers (e.g., a bitter divorce), or just show that a person is living a lifestyle that is not in line with their declared income.
Since businesses need to pay taxes (and most expenses) with money, barter does not help them meet those obligations. However, it has its uses. For example, a new firm will likely not be profitable for some time, so it will have no tax payments due. It might use barter transactions to preserve cash. Established suppliers might agree, as they want a new potential customer to succeed.
But since retail firms have to pay value-added taxes (sales taxes) with money, they have no incentive to offer customers the ability to barter. Furthermore, those customers could be tax inspectors.