The Talmud states:
Taanit 3a-3b
תנא בטל וברוחות לא חייבו חכמים להזכיר ואם בא להזכיר מזכיר מ"ט א"ר חנינא לפי שאין נעצרין וטל מנלן דלא מיעצר דכתיב ויאמר אליהו התשבי מתושבי גלעד אל אחאב חי ה' אלהי ישראל אשר עמדתי לפניו אם יהיה השנים האלה טל ומטר כי אם לפי דברי וכתיב לך הראה אל אחאב ואתנה מטר על פני האדמה ואילו טל לא קאמר ליה מאי טעמא משום דלא דלא מיעצר וכי מאחר דלא מיעצר אליהו אשתבועי למה ליה הכי קא"ל אפילו טל דברכה נמי לא אתי וליהדריה לטל דברכה משום דלא מינכרא מילתא
It has been taught: The Sages did not make it obligatory on one to make mention of dew and
winds, but if one desires to make mention he may do so. What is the reason? — R. Hanina said:
Because they are never withheld. And how do we know that dew is never withheld? — For it is
written, And Elijah the Tishbite, who was of the settlers of Gilead, said to Ahab: As the Lord the
God of Israel liveth, before whom I stand, there shall not be dew nor rain these years but according
to my word. And it is written further, Go, show thyself unto Ahab, and I will send rain upon the
land. Of dew, however, Scripture does not speak. Why? Because it is never withheld. But if it is never withheld, why did Elijah take an oath on it? — This is
what he conveyed to him [Ahab]. THe dew of blessing also would not fall. Then the dew of blessing
should also have been restored? — Because the difference would not have been discernable. (Soncino translation)
It seems from this passage that one need never make any mention of dew in any prayers, precisely because dew is automatic. Indeed, Rambam writes as follows:
Hilchot Tefilah 10:8
ואם לא הזכיר טל אין מחזירין אותו שאין הטל נעצר ואין צריך בקשה
However, if he omits mention of dew [in the summer], he need not repeat his prayers, for dew is never held back, nor is there a need to request it. (Touger translation)
Why then do many communities recite a special prayer for dew on Passover? One possibility is that even though dew is never withheld, there are different types of dew. As the above Talmudic passage states there might be dew but it might not be "dew of blessing". Thus the point of the prayer may be to focus on getting "dew of blessing" rather than just general dew. Indeed, at the crescendo of the prayer we recite the following three lines:
לברכה ולא לקללה
לחיים ולא למות
לשובע ולא לרזון
For blessing and not for curse.
For life and not for death.
For plenty and not for scarcity. (Artscroll translation)
All three of these statements are not about simply getting dew, but about getting dew that is good for us.
Similarly, R. Abraham Gombiner may have alluded to this when he wrote:
Magen Avraham O.C. 114:4
ומ"מ טוב לאומרו שיהיה לברכה
And nevertheless it is good to say it so that it should be for blessing.
Similarly, R. Yechiel Michel Epstein explains that the reason that we include dew in the request for rain is so that it should be "dew of blessing":
Aruch Hashulchan O.C. 114:6
וזה שאומרים בשאלה ותן טל ומטר לברכה זהו אגב מטר דמבקשים שיהיה גם טל של ברכה דיש טל שאינה של ברכה [גמרא
And this that we say in the request, "and give dew and rain for blessing", this is on account of rain, that we are asking that [the dew] should also be dew of blessing, as there is dew that is not of blessing (Gemara).
Rabbeinu Nissim says something similar but slightly more elaborate:
Ran Taanit 1a in Rif pagination
לפיכך נראה לי דהכי קאמר טל ורוחות כיון שאין נעצרין לגמרי אע"פ שפוחתין ומוסיפין ואיכא נמי טל ברכה דמעצר כדאיתא בגמרא לא חייבו חכמים להזכיר דאין החיוב אלא במה שהוא נעצר לגמרי ואעפ"כ אם בא להזכיר כדי שיתוספו בזמן הראוי להם מזכיר
It therefore seems to me that this is what it means: dew and winds since they are not completely withheld – though they may be decreased or increased and there is also dew of blessing that is withheld as mentioned in the Talmud – the Sages did not require [us] to mention [them] since the obligation is only for that which is withheld completely. And even so, if one comes to mention [them] in order that they be increased in their proper time, he can mention [them].
According to this, the reason why we pray for dew may also be to get more dew, as it is only a minimal amount that is never withheld.
There is also the possibility that the prayer is to prevent bad dew. We find a similar idea in another Talmudic passage:
Menachot 62a
מוליך ומביא מעלה ומוריד [וכו׳]. אמר רבי חייא בר אבא אמר רבי יוחנן מוליך ומביא למי שהרוחות שלו מעלה ומוריד למי שהשמים והארץ שלו במערבא מתנו הכי אמר רב חמא בר עוקבא אמר רבי יוסי בר רבי חנינא מוליך ומביא כדי לעצור רוחות רעות מעלה ומוריד כדי לעצור טללים רעים אמר רבי יוסי בר רב אבין זאת אומרת שירי מצוה מעכבים את הפורענות דהא תנופה שירי
מצוה היא ועוצרת רוחות רעות וטללים רעים
AND WAVES THEM FORWARD AND BACKWARD AND UPWARD AND DOWNWARD. R. Hiyya b. Abba said in the name of R. Johanan, FORWARD AND BACKWARD, that is to Him unto Whom the [four] directions belong; UPWARD AND DOWNWARD, that is to Him unto Whom heaven and earth belong. In the West it was taught as follows: R. Hama b. ‘Ukba said in the name of R. Jose b. R. Hanina, FORWARD AND BACKWARD, in order to keep off violent winds; UPWARD AND DOWNWARD, in order to keep off harmful dews.
R. Jose son of R. Abin said, This proves that even the dispensable rites of a precept [when performed] ward off punishment, for the rite of waving is dispensable in the precept and yet it keeps off violent winds and harmful dews. (Soncino translation)
Here the Talmud assumes that there is harmful dew that is worth being protected from, and also assumes that doing something non-essential can protect against it. Similarly, then, though there is no obligation to pray for dew it may still be worthwhile to pray that we be protected from bad dew.