Dear Rabbi Kornfeld:
Insights to Sukah 25 brought the following:
"HALACHAH: The REMA (Orach Chayim 38:8) cites the opinion of the Ran as the Halachah; when there is a way to fulfill the second Mitzvah while still performing the first Mitzvah in its normal manner, then one is not exempt from the second Mitzvah. Otherwise, he is exempt."
Can this explain why a person who is on a journey - to do some Mitzvah should be exempt from the Sukah? After all the normal way of travelling to do a Mitzva - is, often enough, to go to sleep at night; why should the traveller - albeit to do some Mitzvah - be exempt? It does not interfere with the normal way of "travelling to do some Mitzvah"?
Sincerely, Yeshayahu HaKohen Hollander
See Insights to Sukah 26:2 (part of which is cited below), which I think addresses your point.
(FROM INSIGHTS TO SUKAH 26:2):
This Gemara is cited as Halachah by the SHULCHAN ARUCH (OC 640:8). The MISHNAH BERURAH (640:40) adds that if one can easily find a Sukah without difficulty while on his trip, then he is required to dwell in that Sukah. Also, if he travels only during the day but not during the night, he is Chayav to sleep in a Sukah at night. The Acharonim, though, argue how far the obligation to sleep in a Sukah at night goes. The LEVUSH rules that one is only obligated to look for a Sukah that is already built in the town in which he is lodging, but if there is no Sukah built (e.g. there are no Jews in the town), he is not required to build his own Sukah. In contrast, the MAGEN AVRAHAM rules that he is required to build his own Sukah wherever he lodges. The Mishnah Berurah (in BI'UR HALACHAH) and others side with the Levush, because one is not required to spend half the night building a Sukah to sleep in for one night; rather, one merely has to make an effort to find a Sukah that is already built.