A couple of additional thoughts:
A metal pencil sharpener with a large hole (often only available as a two-hole sharpener). Great for turning twigs into shavings. More surface area should mean they dry faster (once you have an initial bit of tinder going) and catch more easily. Shavings will blow around in even a light breeze though, so think about using pack, bidy or whatever comes to hand to provide a wind break while getting fire established.
Personally I swear by Baddest Bee Fire Fuses. Basically short pieces of cotton cord soaked in wax. They are small, light, easy to add to a firelighting or first aid kit, inherently waterproof (probably not up to being buried or submerged for ages, but certainly can be dunked). You pull the end apart to make it fluffy so it will take a spark, then the wax takes over and provides a good amount of heat to get kindling going.
There's a video here: https://www.youtube.com/watch?v=hucYQijUCqo but in that he shows using a whole long fuse. I tend to use them in about 1 to 1.5 inch lengths and then leave them in the fire, I don't expect to hold it while it's burning. Pretty sure I bought some which were shorter to start with, as I don't remember cutting them down.
I have a couple in various places eg every first aid kit, even have two coiled up in the end of my Bear Grylls flint/steel firelighting tool (not my favourite flint and steel, but bought to review and to have a spare).
Another good alternative to fire fuses would be something like Live Fire which is essentially a tiny tin of waxy fuel. I keep a "sport" sized one of these (the smallest) as an absolute backup in case I really must light a fire for actual survival eg for signalling or to stay warm while waiting for rescue with an injured member of party. I think they are a bit pricey to light fires which are purely recreational. I might even balk at using them to light a fire every night of a multi-day hike just for cooking on. But personally I would probably carry a stove rather than rely on fire as my only option for cooking, although I will often do a bit of both (stove for water boiling, fire for everything else if I can). You can use the lid to put them out so you only use up what you need until fire is established. You could probably re-use the tin by filling with suitable non-liquid "fuel" such as beeswax, petroleum jelly (could melt in warmer summer weather), possibly even alcohol gel (but I would use a ziplock as backup to catch leaks).
A "pocket bellows" is a telescopic metal blowpipe which goes from a few inches (short enough for typical tobacco tin firelighting kit) to about 45cm. Great for blowing on a reluctant fire without getting too much smoke in eyes and lungs - and a fire made with wet wood will tend to be very smoky at first. Also really useful if you are trying for the teepee approach as you can reach in and blow where you need to in the middle of the fire. I prefer the kind with a rubber part to hold so it does not get too hot, but you can go minimalist if you need to really save every gram.