It's never been obsolete, but it has not always been very relevant either. The UN accomplishes more than many people give them credit for, especially in the example of successful peacekeeping operations in a few dozen nations around the globe. With the economy becoming more globalized all the time and with truly global issues such as Climate Change, I would argue that the UN will become actually more relevant in the future than it is now.
If during the Cold War it was the US versus the USSR, now it is just the US with no opposition as such.
If all the members of the UN had an opportunity to use their powers without a few rogue members like the US going ahead with their own plans whether they are accepted by the UN or not, I think we could find the UN proving to be very relevant. And it could offer tremendous benefits to all nations around the World which wouldn't be restricted to providing food and water during times of crises.
According to some theorists in International Relations, the UN was never really relevant. Realists would argue that the UN never had the power to force states to do anything and was therefore obsolete from the moment it was created. I would argue, however, that the UN is actually more important today than at many points in the past.
In the Cold War, the UN was fairly irrelevant. Everything came down to the US against the USSR. Each had a veto in the Security Council and so the UN was hamstrung.
Today, we have a much more multipolar world. In such an environment, the UN matters more. There are many more issues that are not issues of state against state. Instead, we have international issues like global warming and a need for greater development and food production. These are areas where the UN can actually matter. It can help to create and maintain NGOs that can affect these kinds of issue areas.
As the world progresses and state-on-state wars become less common, the world's problems become more amenable to what the UN can actually be good at. Therefore, the UN is more relevant today than it was during the Cold War.