What makes this any different from simply leaving your wallet at home and writing down your private key on the same piece of paper? What use does a hardware wallet serve if you have to write down what is effectively your private key anyhow?
When you press the "create new wallet" button on your HW, the device has collected 128 - 256 bits of entropy from various sources. Imagine a sequence of 0s and 1s.
Then the entropy is hashed and the first 4 - 8 digits (checksum) are appended to the initial checksum.
Then the sequence you have is split into 12 - 24 smaller sequences of bits, of 11 digits each.
Each of these subsequences is converted to a decimal number.
Each of these decimal numbers corresponds to an english word in the BIP-39 dictionary (which is the recovery phrase you refer to above).
Finally, the seed words, plus some salt (the word "mnemonic" + an optional passphrase) is stretched through the PBKDF2 function and a 512-bit seed is produced.
This seed produces the wallet (EDIT: and is stored in the device).
Note: as you can see, if 2 people have the same set of words, they can produce the same wallet, unless they have set an optional passphrase on the last step.
Now, to answer the question:
BIP-39 is a standard that is used to facilitate people when they want to recover their wallet. How? It is (as I explained above) a representation of the initial entropy.
If you wanted to produce the same wallet without a backup of the entropy, it would mean that you have produce the same entropy randomly. It will never happen - it is infeasible.
So the wallet offers you 12 - 24 words to help you recover the wallet in any other device you want, provided that it uses BIP-39.
The HW can have a state, meaning it can remember the private key, but if it gets destroyed, for example, how would you recover the wallet?
I know you think that you could hold a backup of the private key instead of the words, but trust me, keeping track of 64 Hexadecimal characters is much more difficult than keeping track of 12 english words.