general techniques are simple

If you need to open a specific lock, you can use a key that encodes the precise information needed to open that lock. If you need to open five locks, you can carry around a ring of five keys, encoding five times the information of a single key. But if you need to open every possible lock, you don't want to carry around the set of all possible keys;Aside from the practical issue that your keyring would be incredibly expensive and unwieldy, this wouldn't even really solve the problem, because now for any given lock you may need to try every possible key! (half of them in expectation). Paradoxically, the set of all possible keys --- like its complement, the set of no keys --- contains zero information about how to actually open a given lock. We might distinguish between the information contained in the key ring (measured using something like Kolmogorov complexity) versus its development cost. The ring of all possible keys, like Borges' library of Babel, is in the worst possible quadrant, being very expensive to build but containing almost no information. you need a lock pick. Instead of representing the structure of any particular lock, it encodes something general about all locks, namely, that they have pins which need to be pushed into the right positions.

Perhaps a fair comparison of complexity should also account for the knowledge required to use the lock pick, presuming that this is greater than that required to use a key. This will disadvantage the pick somewhat initially, but it will still catch up at some point as the complexity of your key ring increases.

Keys are also not as straightforward as you'd think, since for each key we have to know which lock it goes into, and that may actually be a lot of information if we live in a world with many locks. If you find both a lock pick and an unlabeled key on the streets of New York City, it may actually be easier to learn to get value out of the pick (by developing the skill to use it) than to learn how to get value from the key (by finding the door that it opens). Similarly, you may have thousands of papers each solving a particular class of problem, but for any particular problem it can be more effort to find the paper that solves it than it would be to just solve the problem from scratch.

Of course special-purpose techniques have value! Opening a lock with a pick is more work than using the key, because it requires experimentation to learn the specific nature of the lock, feeling out each pin by trial and error. If you need to open a single lock over and over again, of course the key will be easier. But there's obviously a huge amount of value in being able to open new locks we haven't seen before.