why would you use a TLAM for anti-shipping?

In the 80's there was a special varient of the Tommahawk with a ~450km range and speed of ~0.7 mach, specially designed as an anti-ship version, but was withdrawn from service in the 90's.

As according to my memory of a book I have upstairs.

The TASM?  It's in Dangerous Waters, but the manual says that it has been withdrawn from service and it's only there because of artistic licence.

Because it has far more range than anything the chinese can mount on
a ship.

The TASM isn't in service anymore. But there's no reason why the Navy can't order more if they wanted them, plus upgrades from today's level of technology. Yes, you "should" be able to use a Block 4 TLAM against a large ship that isn't moving too fast. It's supposed to have some sort of optical or IR camera and it can be remote-controlled to hit any new targets that are detected.

Maybe it's because the ruskies, Indians, Taiwanesse and possibly the chinese navies all have supersonic speed ramjet powered anti ship missiles that move at twice or 3 times the speed of the slow cruise tomahawk. If the hostiles approach innocently and come within range of their "ruskie sunburn" supersonic missile range. Then even if the tomahawk or harpoon were fired from the USN vessel, the enemy ramjet missile when fired later would still be able to hit the USN ship before the radar operator learns of any tomahawk strike.

None the less I believe the USN is developing their own "sunburn" or they are going to buy the Taiwaneese design and make it in the USA.

The US Navy prefers to use aircraft to attack enemy warships. They just launch wave after wave of aircraft carrying Harpoons, HARMs, and all sorts of guided glide/free-fall bombs until the enemy vessels run out of defensive missiles. Then it's all over for the bad guys. At that point you can send a helicopter to sink the enemy warship. I think the US Navy should develop a long-range supersonic anti-ship missile, too. It will give them the option to launch a counter-attack within minutes of a surprise attack. Airstrike can take hours to plan, prep, launch, and hit the enemy.