The gemara says that you only make a bracha on a candle when the purpose is for light, but not on something that is lit for utility purposes such as cooking or if it is lit to provide honor to someone (this is how rashi understands, but rabbeinu chananel holds that a candle lit for an adam choshuv is considered for the purpose of light). However, it isn't entirely clear whether one would make a bracha on a light which is lit for a dual purpose such as to provide light and for some type of use.
Rashi (d.h. ha v'ha) writes that if a light is lit to honor an adam choshuv (which he holds you don't make a bracha on) and also to provide light for the chazan who will be eating in the beis hakneses, one does make a bracha on it. So long as it is also there for the purpose of light, a bracha can be made. This seems to fit well with the gemara earlier that said that one cannot make a bracha on the candle of a goy since it didn't rest on shabbos, yet technically after some time passes and the fire is considered to have "new" fire mixed with the original fire, a bracha can be made. We see that we don't require the entire flame to be worthy of a bracha in order to make a bracha on the fire. So long as it has mixed into it a form of fire worthy of a bracha, we can make a bracha on it.
However, the gemara that says a fire that is lit sometimes by day, even if it is being lit on motzei shabbos, no bracha can be made. Rabbeinu Yona writes that even though it is sometimes also lit for the purpose of light and not just for the purpose of honor, we see from here that a candle that is lit for a dual purpose, light and kavod, is not worthy of a bracha.
It seems that Rashi and Rabbeinu Yona argue on a fundamental point. Rashi holds that the halacha is that on a candle that provides light one can make a bracha, therefore even if it also serves another function it doesn't detract from the fact that it is also there for light. Rabbeinu Yona holds that the halacha is that a candle which is there for honor isn't worthy of a bracha, therefore even if it also has a component of providing light, the fact that it is there for honor ruins the ability to make a bracha. The rationale of Rabbeinu Yona would seem to be that since the bracha is to express appreciation to Hashem for creating fire which provides light, we can only make this bracha when it is clear from the fire in front of you that it's purpose is for light. Whenever there is a dual purpose, it isn't clear that the function of this candle is to provide light and therefore doesn't warrant a bracha.