Rosyth is simply not capable of building ships. It is assembling the carriers from large blocks built elsewhere - not an insignificant effort - but a long way from building a ship. There are no major steel production / fabrication facilities and no suitably sized undercover build shed. The crane is a red-herring - nice to have only if you can build large highly outfitted units. You can build units at large facilities round the country and assemble them in Rosyth for something like carrier where there is no alternative. You can't do that cost-effectively for something like a frigate.
It was used for assembly as it was the biggest available dock in a live facility in the country. Refits may stay there - or go elsewhere in UK - Birkenhead and Belfast have suitable docks, as does the Tyne at a push.
Short version is that you can do a lot afloat with UW engineering these days. A Class docking every six years or so, isn't a major drama.