Why would the kohanim be so eager to do the ketores so that they will become rich, did they care about money that much? Didn't they believe that their parnasa was gozer on rosh Hashanah?
See TESHUVAS CHASAM SOFER OC #158 DH RISHON who cites MOED KATAN 28a that the length of one's life, the number of children that one has, and one's material prosperity is not dependent on one's merits but rather depends on one's Mazal. However TOSFOS SHABBOS 156a DH EIN writes that if one posseses a great merit, it is possible that the Mazal will change.
C.S. writes that the opportunity to burn the incense is considered a great merit which is capable of changing the Mazal. This is because the Kohen who burns it receives the blessing of Moshe Rabbeinu himself that "Hash-m blesses his wealth" (Dvorim 33:11) as Gemara 26a states.
Therefore MISHNAH 26a states that only Kohanim who had never previously burnt the incense participated in the lottery because it is almost certain that those Kohanim who had never yet won the lottery always had a hard time making a living. Therefore we try to help them by giving them the opportunity of burning the incense and thereby breaking their bad Mazal.
C.S. adds that even a very wealthy person also requires the merits of the incense because it is possible that the Mazal is fighting against him to try and make him lose his wealth.
Therefore, in the light of the above, the Kohanim did not rely only on the Gezeirah concerning livelihood on Rosh Hashanah but they made an effort to attain the great merit of Ketores because through this it is possible that the Gezeirah can be changed.