The vex have a plan many eons in the making. This plan will weave them into the very fabric of reality and allow them to finally make their emperor of all outcomes.[spoiler]They don't attack Earth because for one, they can't simulate us, so attacking our central cluster would be suicide. For two, they may still yet need us. You remember paradox? They needed us in order to cleanse the Vault. They may still plan to use us in the future.[/spoiler]Now about the heart, the vex had two ways of going about achieving their goals. One way was through math and Science. (The Vault of glass) The other was through worship to a paracasual power. (The black garden) However, it's unclear if the garden's heart was a hive worm or a relic of the Queen of final shapes. But above all, I believe they set up shop here because they knew it was at this spot in the universe where a sort of "endgame" was going to take place. Lo and behold, it was here the traveler decided to stop running, and it is here where gods, monsters, kings, and machines are fighting the ultimate battle for survival.