I wonder if you have considered requiring authors to specify the license their code is under in the ASCL submission form? I think that this would be extremely helpful for authors and code users alike. Unlicensed codes are a problem for users: one cannot assume permission to even use, let alone modify or share the software if it has no license. However, it seems most likely that authors who submit their codes to the ASCL intend their codes at least to be used. If they were required to declare a license, even if that license were "no license" or a restrictive one, permissions for users would be immediately clear.
I see that in the FAQ, there is the following:
How a code is licensed has no bearing on whether it can be listed in the ASCL. Codes can be in the public domain, any open source (e.g., BSD, GPL), or copyrighted. It doesn't matter how a code is licensed; what matters is that a code used to generate results in research be open for examination.
Requiring users to specify a license would not conflict with this. It would simply encourage the authors to consider what permissions they wish to give when they list a code, if any, and would clarify immediately for users what permissions the code gives them.
I looked at the last 10 submissions to ASCL and found that 4 had no license statement at all, so it seems likely that unlicensed codes are pretty common in the ASCL listings.
Sorry if this has been discussed before; I couldn't find any previous discussions.