A good quality knife is important
Two things you need in a survival situation are shelter and fire. If you find yourself unexpectedly stuck outside overnight, these two things will be on top of your to-do list. Unless you have a first aid situation, your first actions should be towards building a shelter and starting a fire. Shelter is protection from the elements and fire gives you warmth, comfort, and the ability to cook and purify water.
Survival kits generally come with all sorts of useful items, but they are lacking in a core component...a good quality knife. Most commercially available kits do include a knife, but this knife is usually not of the top quality type. The reason for this is simply cost. To include a good knife in a kit would drive the survival kit's cost way too high for what most people expect to pay.
In a survival situation, you want a knife you can count on that will not break during heavy-duty use such as batonning or chopping wood. You also want one big enough so that you can quickly cut down branches or small trees for a field expedient shelter.
Knives included in most survival kits are light-duty knives. They are not designed for rugged use. This is acceptable for the most part only because the more complete survival kits already include some form of shelter that will probably last the 3 days or 72 hours most kits are designed for. The idea is that you will be rescued or otherwise get help within that time. Kits also include one or more methods of easily starting a fire.
But if you don't have any survival gear with you, you will still need to make a shelter and most likely a fire. With a good knife, you can do both. Using a knife to make a shelter makes it go much quicker than without a knife or with a light-duty knife. Imagine trying to cut down a 2-inch thick tree with a blade designed only for light-duty use. It will be very difficult and take quite a long time. Time you probably don't have. Plus, you're going to need a bunch of trees or branches, not just a few.
If you need to split wood in order to get to the dry center, a flimsy knife isn't going to do the trick. You want a knife you can pound on in order to break open the small log. Inside is dry wood you can scrape or strip off in order to get tinder and kindling. Starting a fire without dry material is a near futile endeavor, especially if all you have is a spark.
The point is to not count on the knife inside of a survival kit to do hard work. They are great for other smaller chores and can be nice to have but you'll do best by considering them back-ups to your everyday carry knife. Knives inside of commercial kits are there to get you through the hopefully short time you're in survival mode. A good quality knife, however, will last you a long time and can stand up to the rugged use you will need in the field.
If you don't carry a knife, you should start. In the unexpected event where you find yourself needing to survive, a good quality knife will be your best friend. If all I could have was one survival item, it would definitely be the knife I carry with me at all times. If you're prepared enough to have a survival kit, you're way ahead of the game. If you don't, at least you'll have what you need in order to take care of the basic necessities.