DSi common key doesn't allow you to write to NAND on a DSi, let alone the DSi portion of NAND on the 3DS, which is sandboxed anyway. As WiiBricker pointed out, literally all it does is allow you to decrypt content off NUS. He was less correct in implying that it would be more use with an exploit available. That's not really true. With an exploit, you load unsigned, unencrypted code. So you don't need the key for that. As for writing to NAND, pretty sure Nintendo will have learnt their lesson from the Wii and require everything being written to NAND to be signed (the lesson learned being that checks would be more thorough and, y'know, working) as well as encrypted, so again the common key on it's own isn't enough to do that, even with an exploit.
What the common key could potentially be helpful for would be helping to create an exploit by allowing investigation of decrypted code etc.
This is all in reference to DSi. On 3DS, the DSi section is of course sandboxed, so even if you were to achieve all this is wouldn't really be too useful.
