Given a “safe” (meaning: brute-force is your only shot) cryptographically strong PRNG, wouldn't it be safe to encrypt data using the CSPRNG to create a key as long as the data and then encrypt the data by XORing it with the key?
Yes it would.
As CodesinChaos reminded us in his comment:
We call that a (synchronous) stream cipher.
Look up RC4 and A5/1, two of the most statistically popular ciphers in the universe. Also compare to a correctly generated one time pad. Not a lot else to say at this point.
The only secure-proven encryption scheme is the one-time-pad. That uses a key of plaintext-length for XOR-encryption once, else it is broken. If your CS-PRNG is not breakable, in sence of any attacker is able to win the predictable game, it is close to being a OTP.
Now think about you would like to encrypt a branch of Wikipedia. How would you like to (1) store and (2) transport the key secure? How would you make sure that no key is used twice?