Until the early 2000s, homepages simply served to signal to users that the brand was online. Websites didn't do much other than to to say "hey I'm online and here is how you can contact me". This was sufficient until more brands found themselves an online home and homepages then had to turn into brand sales people.
Since then, search traffic is taking users directly into the detail pages. The home page isn't accessed as often and this brings new challenges.
When a user gets to a page they will need instant context so that they understand why they reached the page that they have found and doesn't know the brand that goes with it. Every content page now has to be thought of as an entry point to the brand and needs to fulfill the role also fulfilled by the home page.
Navigational elements such as breadcrumbs can help the user get around the website. Mission statements can also help convey the brand and inform users of what they need to do next. The experience provided by the detail page should be no different to the experience provided by visiting the home page. Consistency in design, navigation, and branding should be rule.
Do we still need the home page? Yes. But consider the many ways that a user might access the website and what cues they might need in order to help them.