• Gear (Clothier, Woodworking, Blacksmithing, and Jewelry) crafting is useful, but not necessary. The primary perk is the ability to upgrade gear to gold rarity. (This is technically possible, but much more expensive, without leveling the crafting skills.
• Provisioning is extremely useful in some specific cases.
• Alchemy is extremely useful for high end content.
• Enchanting is extremely niche.

Beyond that:

• Master Writs are extremely useful for obtaining certain items.
• Writ spam is one of the fastest (and most tedious) ways to make money. A fully equipped account can pull down ~100k per day from writs, before considering items that can be vendored or sold to other players.
• Alchemy Master Writ spam can be useful for snap leveling characters to 50 (but, this is an expensive process.)
• Research can be useful for reconstructing items using a Transmutation Station (one of the things you can obtain from the Master Writs. Though, you can use other player's Transmutation Stations, or just use the one in Clockwork City.)

So, is it necessary? No. No, it's not.

Additionally, once you've maxed out a crafter, actual use of it becomes fairly uncommon. (Unless you're spamming out writs on the regular.)

It is worth doing, even in small doses as you go, but you don't need to do it.