If it's not possible, a hybrid would be needed. Or you have a pretty awkward entry level system, like the 20 GB consoles of last gen. However, gimping the SSD by making it optional is the worst move IMO. Having a small SSD/flash in every machine that can be user upgraded is far better than a base console without.
How many would pay $30 extra for a system that's actually designed for fast storage, and not only offers 20% faster load speeds but super rich worlds streaming resources from storage with super low latency?
As mentioned previously in this thread too, RAM could probably be reduced relative to an HDD based system as there wont' be such a need for data chacheing, so that may even mitigate flash cost somewhat.
Regardless, if low-latency storage is going to be a part of the next-gen architecture, it needs to be present in every console in sufficient amounts to get used. If a SKU doesn't feature flash, the experience will be gimp'd for everyone for the entire duration of the generation. And if your rival does it properly, three years on they'll be showing richer worlds with faster load times easily justifying an extra $30 for their box.