As a European I don't understand why this company exists at all.

It's worth pointing out that TurboTax is just one of their products... even if it went away overnight, they'd still have a lucrative business publishing QuickBooks. It is basically the standard in small business accounting software in the US, and a majority of small businesses probably use it, pay an outside accountant that does, or both.

In the past? Because they make a mostly non-digital system digital and convenient. Currently? Corruption. At least for the TurboTax part of Intuit.

There are multiple similar companies in many European countries, even though the government provides (often somewhat basic) tools to file taxes. A large percentage of citizens in the Germany and Austria use paid software because it's more comfortable, same in the UK and Poland. But yes, it would be better if that was not the case, like in Scandinavia.

Has anyone in these comments ever heard of QuickBooks?

Same as Russian. The state provides all needed software for filling documents related to taxes. It's been so for at least 15 years, most likely longer.