As the other answers note, from a legal perspective, it's not a visa because US law says a whole bunch of things about visas, and none of them apply to ESTA and the Visa Waiver Program (there are particular differences about one's right to appear before an immigration judge or to change status once you're in the US, for example). An ESTA is also different practically. To get a US visitor visa, you fill out a big long application, obtain various documents, show up in person for an interview, pay a fairly expensive fee, provide biometrics, wait a while, etc... From many countries, there's a high rate of refusal. To get an ESTA, you fill out a form online, pay a few bucks, and unless something unusual happens, you're approved automatically. So there are some differences there.
But there's a broader issue at play. Visas have historically been issued on the basis of reciprocity (with many, many exceptions in the name of making money and foreign relations). For example, the European Union has a visa reciprocity mechanism:
Visa reciprocity is a fundamental principle of the EU's common visa policy and an objective which the Union pursues in a proactive manner in its relations with non-EU countries. This principle means that the EU, when deciding on lifting the visa requirement for citizens of a non-EU country, takes into consideration whether that non-EU country reciprocally grants visa waiver to nationals of all EU Member States (except the UK and Ireland who do not participate in the common visa policy). The principle also applies to every non-EU country whose citizens already have the right to travel to the Schengen area without a visa.
The current visa reciprocity mechanism (Regulation (EU) 2018/1806) requires Member States to notify cases when non-EU countries, whose citizens can travel visa free to the EU, require visas for EU nationals. If such a country does not lift the visa requirements within 24 months since the notification by a Member State of a case of non-reciprocity, the Commission can temporarily suspend the visa waiver for 12 months for nationals of that country. In doing so it must take into account the consequences of the suspension of the visa waiver for the external relations of the EU and its Member States.
In other words, if you impose visa restrictions on us, we'll impose them on you (in reality, that doesn't exactly happen, and you can scroll down in that article to see how, essentially "we're working on it" is used as a cop-out, since ending visa-free access for US citizens visiting Europe is not actually something the EU wants to do).
When the US started the ESTA program in 2008-2009, it wanted to add an additional pre-screening step to stop certain travelers from even getting on a plane to the US, but it didn't want to upset the entire reciprocity mechanism it has with countries around the world. This wasn't a novel idea—Australia instituted a similar system some years before. So calling it an ESTA and explicitly saying it's not a visa was a way for everyone to save face diplomatically. The US could get its ESTA program, and every other country could give a wink and a nod and say "since you're not imposing a visa requirement on our citizens, we won't impose one on yours." And in subsequent years, more countries have imposed ESTA-like "not a visa" requirements, such as the EU's forthcoming ETIAS system.
So yes, from the perspective of a traveler, an ESTA looks rather like an easy-to-obtain visa for the reasons that you mention. But from the perspective of a country's government, an ESTA looks dissimilar enough from a visa that the requirement could be imposed without great impact to foreign relations.
