The Oral Torah being passed down orally, it is naturally subject to certain amounts of corruption via malicious distortion, improper application, simple forgetfulness, etc. The existence of a Written Torah can be seen as a protective measure against this. When someone forgets something, distorts something, or misapplies something from the Oral Torah it is hard to fight against it. You can't really prove that something not written down anywhere is one thing over some other thing. With a Written Torah, the basic fundamentals always exist in writing. If someone distorts, forgets, or misapplies something, everyone else can just refer back to the text and point out the truth.
We can see a prime example of this from the following Talmudic passage:
Temurah 16a
אמר רב יהודה אמר רב בשעה שנפטר משה רבינו לגן עדן אמר לו ליהושע שאל ממני כל ספיקות שיש לך אמר לו רבי כלום הנחתיך שעה אחת והלכתי למקום אחר לא כך כתבת בי ומשרתו יהושע בן נון נער לא ימיש מתוך האהל מיד תשש כחו של יהושע ונשתכחו ממנו שלש מאות הלכות ונולדו לו שבע מאות ספיקות ועמדו כל ישראל להרגו אמר לו הקב"ה לומר לך אי אפשר לך וטורדן במלחמה שנאמר ויהי אחרי מות משה עבד ה' ויאמר ה' וגו' במתניתין תנא אלף ושבע מאות קלין וחמורין וגזירות שוות ודקדוקי סופרים נשתכחו בימי אבלו של משה אמר רבי אבהו אעפ"כ החזירן עתניאל בן קנז מתוך פלפולו שנאמר וילכדה עתניאל בן קנז אחי כלב (הקטן ממנו) [ויתן לו את עכסה בתו לאשה
Rab Judah reported in the name of Rab: When Moses departed [this world] for the Garden of Eden
he said to Joshua: ‘Ask me concerning all the doubts you have’. He replied to him: ‘My Master,
have I ever left you for one hour and gone elsewhere? Did you not write concerning me in the
Torah: But his servant Joshua the son of Nun departed not out of the tabernacle? Immediately the
strength [of Moses] weakened and [Joshua] forgot three hundred laws and there arose [in his
mind] seven hundred doubts [concerning laws]. Then all the Israelites rose up to kill him. The
Holy One, blessed be He, then said to him [Joshua]: ‘It is not possible to tell you. Go and occupy
their attention in war, as it says: Now after the death of Moses the servant of the Lord, it came to
pass that the Lord spake; and it further says; [Prepare you victuals for within three days, etc.].
It has been taught: A thousand and seven hundred kal wahomer and gezerah shawah and
specifications of the Scribes were forgotten during the period of mourning for Moses. Said R.
Abbuha: Nevertheless Othniel the son of Kenaz restored [these forgotten teachings] as a result of his
dialectics, as it says: And Othniel the son of Kenaz, the brother of Caleb, took it; and he gave him
Achsah his daughter to wife. (Soncino translation)
Here we see that many laws were forgotten after the death of Moses. But as long as there was a Written Torah, almost everything could be rederived from the text. Without a Written Torah, we would be at the mercy of people's memories.
In addition to the fact that the Written Torah helps keep the Written Torah from being forgotten, it also actually helps the Oral Torah from being forgotten. This can be seen from the fact that the Sages often linked things back to the Written Torah even when there was not necessarily a real connection. Several authorities point out that this is to make it easier to remember. (I.e. if the something is linked to a written text, when you see the written text you can be easily reminded of the linked information.)
For instance, in reference to the hint to the Seven Noahide Laws in the verses of God's commandment to refrain from eating from the tree in the Garden of Eden, R. Judah Halevi writes:
Kuzari 3:73
There is a wide difference between these injunctions and the verse. The people, however, accepted these seven laws as tradition, connecting them with the verse as aid to memory. (Hirschfeld translation)
Rambam in his explanation of the rabbinic concept of asmachta writes:
Commentary to Mishnah, Introduction
והיתה התשובה על זה שהם הלכה למשה מסיני ואין להם שום יסוד שילמדו ממנו באחת המדות ואין להם רמז בכל התורה אלא הסמיכום לפסוק זה כעין סימן כדי שישמרום ויזכרום ואין זה מענין הפסוק וזהו ענין אמרם קרא אסמכתא בעלמא בכל מקום שנזכר (Kafih translation)
And the response to this was that they are halacha l'Moshe m'Sinai and they have no foundation from which we can learn via one of the methods [of derivation], and there is no hint to them in the entire Torah. But [the Sages] connected them to this verse as a sort of mnemonic, to ensure that they would be protected and remembered, but they don't [actually] have anything to do with the verse. And this is the meaning of their statement "the verse is a mere asmachta" in every place it is mentioned.
Ralbag actually explicitly states this point when he explains why he derives all the details of mitzvot from the plain meaning of the verses (rather than using the methodology of the Sages):
Commentary to Torah, Introduction
והנה בסמכנו אותם הדינים לפשוטי הכתובים תועלת להשאיר יותר זכרון אלו הדינים בנפשותינו כי פסוקי התורה אפשר שיזכרו בקלות לרוב התמדתינו בקריאתם וכאשר יוצאו מפשטי הכתובים ההם ביאורי המצוה יהיה זה סבה אל שיזכרו ביאורי המצוה בכללם עם זכירת הפסוקים ההם
And connecting those laws to the plain meaning of the verses is a help to better solidify those laws in our memory, for the verses of the Torah can be easily remembered due to the consistency of our reading them. And so when elaborations of the mitzvah are derived form the plain meaning of the verses it will be a cause of remembering all the elaborations of the mitzvah when remembering the verses.