Carved or brought still makes no sense
Why?
When have vanity or religious projects and monuments made "sense", people have worked out a number of ways they could have been built, oddly enough most of the "impossible" aspects are only "impossible" if you don't take into account the resources of the time, or the way we've got documented examples of it being done on smaller scales.
The materials were basic, they had IIRC good transport links for shifting people and materials over long distances and we've got examples of the vessels they used, and there are examples of the progression of the pyramids including at least one "oopsie" that they didn't pull down indicating they were learning how to build bigger/more impressive.
There used to be a show on IIRC C4 or BBC2 where they would get together a bunch of historians specialising in the period, a bunch of engineers/builders/craftspeople and they'd try and work out (and ultimately demonstrate) how some of the "mysterious" and "fabled" structures could have been assembled using methods, tools and materials that they knew were present in the area at the time. It turned out that quite often the "impossible" was possible if you had experience and an understanding of what was being done, the problem was usually the level of manpower involved, but the Pharos had basically an entire country to call on.
This is before any consideration of the fact that we know we've lost a lot of skills and knowledge even from just a few hundred years ago in the West because people didn't record it, so the idea that "there wasn't a record of how they built them" in itself is meaningless as there are a load of things from the Roman times that we're only just learning now* and they kept fairly good records (I've seen archaeologists joking that "it's yet another roman villa" when talking about what they're doing this year).
IIRC it's the sort of reason that the likes of English Heritage keeps a list of "endangered skills", as although they're documenting them they know some things will be lost when the last people that currently do it die, unless they train replacements, and they know that we have lost the knowledge of how some really common things were done in the past (people don't tend to record something they do without thinking and are used to seeing every day).
*IIRC one of their concrete mixes was only recreated a few years back, and people keep finding a specific type of odd artifact that no one can agree what it was for as there aren't any records for it, except they do know it was fairly widespread as they've found examples all over the place.