First they propose a genetic code that is totally unrelated to the current one. It can be perfectly the table of a totally different lifeform. The transition they propose looks too difficult, almost impossible.

Probably we had a transition from RNA to DNA a loooong time ago, but they have a 1 to 1 translation, and the intermediate steps look useful. But no one is sure anyway.

They propose a change where almost all the table changes and almost all the internal structure of the table change.

It is very strange that they have 20 amino acids and no stop code. A proposal with 19 amino acids and a stop code looks more sensible. We know that it is possible to add new amino acids to the table (with enough time). I think the main problem is that using 19 amino acids and a stop code breaks the magical part of predicting the number 20 with pencil and paper.

To make the table work, you need the correct transfer-RNA. To get all the symmetries in their model you need to be really lucky. In the block model of 15+1 you any random selection of tRNA is fine if it ignore the last base.

Another big problem is that they predict that half of the proteins would have been constructed backward. But as they say this make proteins not fold correctly. They try to avoid the problem using palindromic proteins, that is not supported by evidence.