The term "hypersonic" is not a particularly helpful one. The generic term refers to an missile system traveling faster than Mach 5, but there are 3 distinct types of weapons that fall into this category, which are very different.

1. Ballistic missiles: most ballistic missile systems are hypersonic. We've had ballistic missiles since WW2, the very first American ballistic missile (the redstone) was hypersonic, and that was back in the 1950s. This is not new. People make a lot of missile like the Khinzal, but this is just an air-launched version of the Iskander missile, which is from the 1990s.

2. Hypersonic glide vehicles: normal ballistic missiles drop a re-entry vehicle that just falls to earth. It might have some stabilizing fins, and some ability to make minute adjustments to its course to improve accuracy, but this is limited. In a hypersonic glide vehicle, the re-entry vehicle is meant to be more of a glide body, and is able to make actual maneuvers and turns. The technology here is also not new. For example, the Space Shuttle is an example of a hypersonic glide body. Research in this field has been around for a long time, though it's only in the last few years that countries have begun actually fielding weapons featuring glide vehicles. The annoying part with this is that the term "hypersonic glide vehicle" implies that the reason these are so difficult to intercept is because of their speed. But it's actually the opposite: in order to maneuver, a hypersonic glide vehicle actually has to travel slower than a traditional ballistic re-entry vehicle! The advantage of a HGV is not its speed, but its ability to maneuver, which makes it harder to intercept.

3. There are also hypersonic cruise missiles. These are missiles that use ramjet or scramjet engines to fly at hypersonic speeds. These tend to be even slower than HGVs, and will have much shorter ranges because they have to consume fuel to maintain this speed. Several of these are in development, but I don't believe any have been fielded. The main advantage of these is even further maneuverability, and a lower flight altitude which should make them harder to detect. Additionally, because they are flying in the atmosphere, it requires a different type of interceptor to defeat.

There are trade offs. That missile is expense and (see other discussion) might not even hit. A ship is mobile and moves erratically - the enemy needs to find it (not as easy as it sounds even with satellites all over). A missile that lands in the sea 100 feet from a ship does no damage. Hyper sonic often means limits to how you can maneuver it, so you have a chance of figuring out where it can be and thus getting the ship away (depending on your ability to detect it and predict where it is going). The rest of interception was covered by other comments.

A ship lets you get closer to the action. The closer you get the easier it is to overwhelm electric warfare - either because the slow drones can be programed and so don't need a radio (or fiber connections), or because you can make your signal strong enough to overcome it.

Missiles don't have infinite range. Different ones have different limits. Longer range costs both more money and payload. A ship can laugh off anything a tiny drone can do (even a commercial ship).

The above are all trade offs. However navy warfare is not dead and unlikely to die.

Yes. Patriot has intercepted Kinzals in Ukraine (and older versions of Patriot at that), so the tech is well established. SM3/SM6 missiles on Aegis equipped ships can defend themselves against hypersonic missiles.

CIWS does a pretty decent job but the reality is that a hypersonic missile would be met with a large nuclear response as it's a first strike weapon.

If you can read between the lines of the posture reviews, any potential full scale war with China would include a massive nuclear first strike by necessity.

Everyone is aware of this and is avoiding a large scale engagement.

Most likely a regional war with China (probably over Taiwan or less likely, the Philippines) would draw in lots of regional players because everybody want's to pick China apart.