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Depends on what's "high frequency" for you. CRGO (cold rolled grain oriented steel) is preferable below 10 kHz, it's usage may be reasonable in some cases at 10 or 15 kHz. Respectively low sheet/tape thickness (e.g. 0.1 mm) required to reduce eddy currents.
Yes you can, but the problem is that it saturates at extremely low flux densities compared to any of the metal cores. Its just totally impractical for size and cost reasons at 50Hz in any transformer.
Normal common 0.3mm grain oriented silicon tape wound power cores are commonly used up to 400 Hz power line frequencies, but are very useful a fair bit higher than that.
As FvM says, really thin silicon tape like 0.1mm will take you right through the whole audio range, assuming that is your area of interest.
The cores are available, but cost more than the much more common power cores.
Ferrite is just not practical below several Khz because of the very early saturation problem, and that gets even worse as the frequency goes even lower.