In my time as a student buddhist society secretary, I recall we asked a number of ethnic monks to come and give a talk. As long as we could provide transport, all obliged. So like others have said, if asked monks do tend to share the Dhamma to the best of their ability, which is more in some cases than others.
Should there be more effort made to reach out to Westerners? Maybe. Some temples are already run off their feet catering to their ethnic community's needs. Others are more on the lazy side.
C'est la vie...
PS. On retro's side of town, I only know of an active Vietnamese temple of Ven Phuoc Tan (where Lawrence Mills (Phra Khantipalo) stayed for some time) who does a lot of work in Vietnamese community but also does things with Westerners. He is more Mahayana though, I believe. On this side of town, there is Dhammasukkha of Ven U Pandita I mentioned earlier who runs classes in English. So things do happen. I am sure there are many more I am not aware of. Of course the quality of the monks and their level of commitment to the Dhamma varies, but so does the quality and commitment of the lay practitioners.