The original question conflates domain names and their relevance in search results as a metric of their importance.
TL;DR : Google serves relevant information and knowledge sources, regardless of name. Domain names on the other hand, identify resources by mapping host names to numerical IP addresses. While those are related, they are very different animals and have different purposes. Apples to oranges.
The long:
Generally speaking, domain names are as important as your name would be to you. You'd wish you had the best, greatest, badass name there is, but you make do with what you've got. Ditto for company names. Companies live and die by their operation and all the myriad business factors for which company names are but one among a long list. But doggone it sure wouldn't hurt to have a nice name, would it? An identity no one else can have.
I see OP's point about domain names as it relates to SERPs, and in this case, it is a totally different point. Looking at it from this narrow lens, Google is not in the business of vanity names or in caring about domain names. It's people who care about names, and this is why it's important, not for Google, but for whatever help names give in stacking the odds on your favor for identifying things like websites.
Google itself has a very different objective: serving answers, info and knowledge to its users of the utmost relevance, context and authority at the point of the search. This includes divining a searcher's true intent across misspellings or contextual cues (e.g. When you search for 'apple' it has to disambiguate if you mean the fruit, or growing the fruit, or the tech company, or its stock price, or its many products for example; and displaying the most likely items you are actually looking for). And Google isn't the only source of this information or traffic. Social media and other sources drive millions of traffic, and these don't take away nor vice versa, necessarily enforce the need to use domains.
So domain names will be very relevant for a long, long time to come. They are not "needed," as an absolute point, but are extremely important for its purpose, and to simplify and identify things much better as far as universal resource locators/identifiers go, cloud or otherwise. Using numbered directories, for example, would be having it backwards.