Why didn't Jesus write down a gospel for himself instead of relying on others to record his words? Surely this would have prevented a lot of grief and dispute over his words later on, right?
This is actually a very good question, but it is one that does not take into account the social background data. There are two factors that should be taken into account:
The prevalence of orality over writing in ancient society. Today transmitting something orally is considered equal with not relaying it in a trustworthy manner, and we demand to see things "in writing" before we believe them. As hard as it may seem to believe, exactly the opposite was true in ancient times.
Ancient literacy was no higher than 10 percent at any given time, so the primary method of communication was oral. Memory capabilities were correspondingly much stronger, so that it can not be said that oral transmission was unreliable, or that because something was important, it "ought to have been written down". Neither Jesus nor anyone else in ancient society would share this modern sentiment.
The role of scribes. Related to this, the rarity of literacy made for an excellent business of scribal activity. And the paradigm of the day did NOT require that a teacher be the one writing down his own works -- rather, he would hire a scribe to do it as he recited his teachings.
The role of Matthew in this regard is quite obvious and mirrrors precisely the scribe/teacher relationship of Jeremiah and his faithful scribe Baruch. And as one commentator pointed out, wouldn't Jesus' time have been better spent preaching and healing anyway, rather than pursuing the laborious task that writing was in those days?
This point is further elucidated by Achtemeier in his article "Omne Verbatim Sonat" (JBL, 109, 1990, 3-27). He stresses that in antiquity the "normal mode of composition" was to dictate to a scribe. "Dictation was recommended over writing in one's own hand by Dio Chrysostem, and famous personages, we are told, were regularly accompanied by a slave prepared at any time to take dictation" -- even if they were on horseback, or in the public baths.
Though there was some disagreement on this preference (Quintillian preferred writing himself to dictation), it is clear that Jesus "doing it himself" was not a requirement.
Thus the general objection that Jesus did not write anything misses the point, because it anachronistically assumes a modern view of the importance of writing upon ancient peoples.
One added point about the idea that if Jesus had written things himself, it would have meant less controversy over what he said: I doubt this would stop critics, who could just as readily use such rationalizations as, "It was added by a later writer" -- just as they do now -- for lines they found objectionable. I can also see them questioning the authenticity of such works just as readily.
But if that is not enough (as it should be), then let us ask this: Why didn't Socrates write anything down himself, either?
For more on this, see here. For a full overview of the ancient view of writing as a less-trusted "supplement" to orality, see Tony Lentz, Orality and Literacy in Hellenic Greece.