1) If someone is aware enough to want to be baptized without any pressure or coaching from others, and if there are no "worthiness" issues that would prohibit it, I have no problem whatsoever with that person being baptized.
2) We teach that up until baptism at the age of eight, the kids who are baptized haven't been accountable up to that point - at least not in the same sense as converts who are baptized. Thus, really, what's the difference between the standard eight-year-old baptism and baptism for someone who isn't accountable after being baptized?
3) We teach of the need to avoid being baptized "unworthily" - and it's hard to say someone who is not accountable is "unworthy", in the classic, traditional sense of how that word is used.
4) Baptism, the Priesthood, temple attendance and marriage are very different things, and I don't want to deny one simply out of concern about the others.
5) I understand, however, the concern that baptizing those who are not considered to be accountable could perpetuate the idea that they need to be baptized and, eventually, that they (and, by extension) all people actually are accountable from birth, no matter their capability to understand. I also understand that if one such person is baptized, others who have loved ones in similar situations might feel like those loved ones also should be baptized. Therefore, I understand the desire to maintain a bright line with those who are believed not to be accountable. It can be a can of worms that isn't worth opening.
I would have no problem baptizing someone who wants to be baptized - and if someone understands enough to feel like he isn't a "real member", I think he understands enough to be baptized. However, I personally would do it as a clear exception to the general rule - and, if I were the Bishop, I probably would announce the baptism much like if it were a convert baptism and say something very direct, like:
Billy has come to me and asked to be baptized. After talking with and interviewing him, I believe he understands the purpose of baptism well enough and is fully worthy to be baptized. Therefore, his baptism will occur at such a time.
However, having said that, I would support a Bishop completely and without hesitation who felt like he couldn't make an exception - even though I believe exceptions often are what give real meaning to the rules.