Does anyone comment on why Yonah needed the kikayon when he already had shade from his sukkah?

Question

In Yonah 4 verse 5 says:

וַיֵּצֵ֤א יוֹנָה֙ מִן־הָעִ֔יר וַיֵּ֖שֶׁב מִקֶּ֣דֶם לָעִ֑יר וַיַּעַשׂ֩ ל֨וֹ שָׁ֜ם סֻכָּ֗ה וַיֵּ֤שֶׁב תַּחְתֶּ֙יהָ֙ בַּצֵּ֔ל עַ֚ד אֲשֶׁ֣ר יִרְאֶ֔ה מַה־יִּהְיֶ֖ה בָּעִֽיר׃

Now Jonah had left the city and found a place east of the city. He made a booth there and sat under it in the shade, until he should see what happened to the city.

So Yonah had shade in his Sukkah. Verse 6 says:

וַיְמַ֣ן יְהוָֽה־אֱ֠לֹהִים קִיקָי֞וֹן וַיַּ֣עַל ׀ מֵעַ֣ל לְיוֹנָ֗ה לִֽהְי֥וֹת צֵל֙ עַל־רֹאשׁ֔וֹ לְהַצִּ֥יל ל֖וֹ מֵרָֽעָת֑וֹ וַיִּשְׂמַ֥ח יוֹנָ֛ה עַל־הַקִּֽיקָי֖וֹן שִׂמְחָ֥ה גְדוֹלָֽה׃

The LORD God provided a kikayon , which grew up over Jonah, to provide shade for his head and save him from discomfort. Jonah was very happy about the plant.

There seems to be a clear question, “If he had a sukkah with shade, why did he need a kikayon?” and a simple answer - “The kikayon gave valuable extra shade.”

Is there any commentator who asks the question? I am not satisfied with the simple answer.

Answer 1

Radak says:

ואף על פי שעשה לו סוכה לצל, אולי יבשו עצי הסוכה, כי ישב שם עד מלאות לו ארבעים יום.

And Mezudat David:

כי צל הסוכה הוא דבר שאינו מתמיד, כי הולך ומתייבש מחום השמש; ולא כן הקיקיון, היונק רטיבות הארץ.

Both explain the fronds Yonah put up dried out (Since he apperantly waited there for some time), and he then needed​ another solution.