Silicon transistors with such gate lengths would not work, because the too short gate could not close the conduction channel (the minimum gate length with silicon is likely to be greater than 10 nm, even with gate-around transistors).

The masks used for deep UV lithography or for any other kind of high-resolution lithography are also made with electron-beam lithography.

Therefore it is obvious that anything that you can do in a form of lithography that uses masks you can do with electron-beam lithography.

Using directly electron-beam lithography skips the production of masks and their use.

This is a huge cost reduction in the cost of processing a single wafer (which may have hundreds or thousands of chips). However the processing throughput is orders of magnitude lower than when using masks. For very high-volume production, the costs of the masks and of the deep UV lithography are divided over millions or billions of chips, so they are reduced to a reasonable fraction of the cost, which is compensated by the high productivity.