Can G300/700/900 series arrays be run and managed without SVPs?
Yes. The SVP is technically optional. You can use HSA, HCS, or CCI to manage multiple arrays. You can also use HSA Embedded, which is already running the controllers, to manage an individual system. See the Product Overview for Hitachi VSP G/F350, G/F370, G/F700, G/F900 and Hitachi Storage Advisor Embedded Guide. Some features/operations may require Device Manager (either HCS's HDvM or Storage Navigator) though.
...Hitachi supplied SVPs being woefully underpowered...
Haven't heard of this being an issue; but if you'd like, you can configure your own server or virtual machine with beefier specs to function as an SVP. Check out Chapters 5 through 8 of the Service Processor Technical Reference