Because if Aquamarine and Topaz never return to Homeworld, then Homeworld is just going to send retrieval scouts like the Rubies to go rescue them, same as they did with Jasper. And Aquamarine and Topaz seem like they must be much more valuable than Jasper, since they were sent by Diamonds personally, so it's likely they wouldn't just give up on getting them back. For every crew Steven converts or disposes of in some way, Homeworld is going to eventually notice and wonder what's up, and just keep sending more. For a long time he's tried diffusing situations by putting bandaids on them, and it's about time he tried a real fix for once. Steven possibly decided that Homeworld is just going to keep coming again and again on increasingly worse missions if he doesn't do something, and the something he decided to do was to turn himself in in exchange for Homeworld finally leaving Earth alone. It's not much for him to go on, since Homeworld is powerful enough to just capture him and then continue to do to Earth whatever they please, but he's a naive kid who often takes people at their word, and he's the only bargaining chip he has.
Also, Topaz probably didn't volunteer to go to Earth in the first place because she thinks the Cluster is still going to blow it up. Inviting Topaz to Earth would mean explaining that the Cluster has been neutralized, and doing so is a pretty big risk if he can't be 100% sure of Topaz's loyalty to Earth and ability of keeping that vital info from leaking to Homeworld through Aquamarine if they couldn't manage to bubble her. If Homeworld finds out the Cluster isn't coming, they'll send somebody to unbubble it, and then the Earth is fucked.