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Using neutrinos is far less efficient than using gamma radiation or neutrons or high energy electrons or ions for transmutations.

The photons/neutrons/electrons/ions have a high probability of interaction with the target, while the neutrinos have a very low probability of interaction.

All the elements that do not exist in nature due to low lifetime have been produced by transmutation, but this can be done only for very small quantities at huge prices.

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Thanks for a great couple of replies. I'd just add that there are almost certainly more superheavy elements not thought to exist in nature which have yet to be produced artificially, but probably will be at some point.

... but which instantly decay. So not interesting.

There are definitely unstable superheavy elements that have never yet been produced, or at least detected, but the interesting prediction (widely accepted, but far from proven) is that there are some stable ones.

[0] https://en.wikipedia.org/wiki/Island_of_stability

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