Why dont Jews want converts but then do accept them?

Why is there conversion if a gentile can make Hashem happy in his way which is equal to that of Jews? And if Judaism truly says they don't want converts, than why are they even accepted at all? It doesn't seem consistent. The only reason I can find is so that they want to do more mitzvot to make God happier.

God is perfect and doesn't "need" us to make Him happy. We all, Jews and gentiles, do mitzvot because of the eternal Godly ideals involved, that we totally identify with, and are for our benefit. Nevertheless, the Nation of Israel has a unique role as the "Light for the Nations" to bring monotheism, morality etc. etc. to the other 99.8% of mankind, raising them little by little to be that much more Godly and good. For this unique role, God gave Israel many more & difficult obligations, both individual and national which change every aspect of our daily lives, and also runs our history in a totally different, often more difficult, way. Gentiles, who comprise almost all of mankind, are meant to observe the 7 Noachide laws, and there's no reason to do more, for that's exactly what God wants of normal people. Nevertheless, if some of them individually, adamantly wish to join the Jewish Nation, we are not racist, and it would be unfair & immoral to deny such an aspiration. Nevertheless, there really is no reason for them to do so, for God loves them as He created them!