That is, God sent a line of prophets, such as Moses, etc. and it would seem that he gave up on them, and started sending a prophet to a totally different people; the Arabs.
There are some very logical reason why He sent the Quran through an arabic prophet (through the linage of Ismail) rather than one through prophet Issac's linage.
I'm sure you know the fact that as a test, the Creator brought the Messiah to the Jews who was in their linage, but didn't have a father, and they rejected him, claiming that Mary committed fornication-- despite the Messiah uttering truthful information.
In the same manner, the Creator sent them another prophet from linage of prophet Ismail, who wasn't wealthy like them, but uttered truthful information. Some accepted his message, but quite a few didn't for the very same reason you've suggest. This was all a test, to see if the Jews (the shallow ones) would stop focusing on the exterior (ie. raving about the claim of being the chosen people) and instead focus on the interior (ie. that all people of good morals/faith are equally blessed by the Creator-- no race is superior to any other race).
Another reason as to why the Quran was sent through an Arabic prophet, is because their is a very mystical/mysterious feature behind the Arabic language, just like there is with the Hebrew language.
In the Torah, you will see that some of the letters have crowns on them, and there is a quite a mystery about it. Some Jews believe that these crown-let words will reveal secrets about the Creator's way.
In Arabic, the word Allah has an isolated crown-like symbol on top of it (known as shadda). This was not a coincidence, there is a very important reason for it. Whatever the reason it may be, there is a high probability that someday it will answer the mystery about the crown let words in the Torah. It's like a key and it is addressed in the arabic quran.