Oddly enough it actually is possible.
Antimatter is only 3 orders better than fission, 2 orders better than fusion.
Which means if your antimatter reactor runs on grams of it, and the rest of the weight is the shielding needed, while the fission reactor runs of Kg’s of it but doesn’t need as fancy shielding, then you actually have the same output using similar weight reactors.
EVE tech also doesn’t really meet the requirements for Dyson structures. We haven’t the ability to scale the tech up enough for that. It’s heading that way but we simply can’t produce things big enough to even start. Stations might be ‘huge’ but they are island/city sized. All the stations in New Eden wouldn’t even be 1% of 1% of 1% of a Dyson structure.
So yeah. Logic wise it makes sense why we don’t use solar, or rather logic would say that the solar already exists and is why Citadels don’t go totally offline when out of fuel, and game mechanics wise it would make there be only one sensible point to anchor your structures and you just use a few more to get the services/rigs you need for whatever you are doing if you have to.