In the constrained based model community there were/are some efforts to convert SBML to JSON for serialization. I was part of some of them so if you are only interested in constrainted based models there are solutions already (i.e. SBML core level 3 + fbc package).
I can only highly recommend to not touch JSON serialization, but stick to XML/SBML. One argument is JSON serialization for the web, but you can just consume the XML with Javascript and you are good.
To give an example of all the problems you can have a look at the cobrapy issue tracker and basically half of the issues are related to incorrect/problematic JSON encoding.
Main issues coming up are invalid SIds, because JSON is not enforcing the ids of SBML (you see this problem a lot with BiGG models) and problems with NaN which cannot be encoded in JSON. As a consequence ids are replaced with prefixes which creates a ton of new issues.
Also validation becomes a big issue. You have very good validation for SBML, but would need to create a JSON schema and validator for your SBML files.
In summary, don't do JSON serialization of SBML if your life not absolutely depends on it. The long-term issue and maintenance are a nightmare.