The reason a website needs verification goes back to what a search engine is and Google is a search engine. A search engine has a software program called a Crawler. This program’s job is to find every website on the internet and store its content in the search engine’s database.
So that when a user searches for something in the search engine, it can get the most appropriate pages to answer their query. Now, as there are hundreds of millions of websites if not more, getting to know what new website is added to the internet is a massive exercise and tough.
This may result in the Search Engine Crawler reaching your website months after its launch, rather than days. However, if your website domain is linked to a well-known website already in the search engine's database, and the crawler discovers your website link within that website's pages, the crawling process may occur sooner. This highlights the importance of backlinks.
Also, finding websites is costly in terms of compute power. Since, all websites wants to get discovered as soon as possible, Search Engines have come up with a solution to make finding websites cheaper! They said, "Please come and tell us about a website you have (aka verify your site with Google Search Console) and help make our job easier. In return we will give you insights to help you write content that targets search engine intent (and ultimately help make our job EVEN easier)".
So it’s a win-win, verifying a website with a search engine helps the website get discovered faster and search becomes better.
As mentioned earlier running a crawler is really expensive and also consumes a lot of energy (think electricity). Ahrefs a prominent SEO software, that runs its own crawler to mimic how a search engine works and provides business intelligence to rank higher in search rankings, recently published how it cost them almost ~$40 million to run such an infrastructure. Apart from the monetary cost of running such an infrastructure the implication of using electricity and cooling for data centres is at a huge cost to the environment. In fact, a very crude calculation tells us that for every 1$ spent in a data centre, almost 4kg of CO2 is generated.
We can extrapolate the environmental cost of running a search engine.
If your website is built with Konigle, here's a simple way of verifying your website with Google.