L is justified in assuming humans by the decision-theoretic consequences: he likely can do nothing against supernatural entities (and IIRC, even in the extremely difficult scenario of killing a shinigami, that doesn't stop the killings with Death Notes), so proceeding on the assumption that it is a human is better than not proceeding.
Besides that, I don't think L is 'hax'. (Near and Mikami, on the other hand, is a major example of authorial fiat and the part of Death Note I hate the most.)
There are alternatives to a human killer which would provide some opportunity to make headway, which do not have priors that are obviously lower than a human with a supernatural weapon, such as extraterrestrials or some sort of supernatural creature which is humanly beatable.
The first point where I got really pissed off though was when L jumps all the way to "the killer must know the victim's real name" based on the murder of Lind L. Tailor. Lind L. Tailor was a convicted criminal, and L. wasn't, and killing criminals was already Kira's suspect...
The results for these have been stable for a while now; I'm posting them a bit late. 95 people took the survey after I modified it to add two questions. For the public version, I removed the pre-change data (10 data points).
One text response included identifying information, which I removed in the public version of the data. If you participated and there is any information you provided that you would like removed from the public version, PLEASE tell me as soon as possible and I will remove it.
P.S. To the person who predicted an 80-90% significant difference between different parts of California: I predict with at least 90% confidence that there will be no significant difference, because of the wide spread of locations and smallish sample size of this survey.
(The original post about the survey.)
EDIT: After some comments that it was unethical for me to post the data (in particular the text), I removed public access from the link provided earlier. Given my precommitment to post the data, I assumed it was clear enough to respondents that it would be public. I'm not convinced that this has hurt anyone, but given that others seem to disagree, it seemed prudent to remove it. Please feel free to continue this discussion; I'm interested in your thoughts.