How to set simple parameterization for a json_value query (without using plan guides)?
So far I have collected the following workarounds:


Wrap the json_value function in a dummy subquery. For example, 

select  mt.pk

from    My_Table mt

where   (select json_value(mt.json_data, '$.group_id')) != ''

Per David's first comment, try "Optimize for Ad Hoc Workloads" instead of forced parameterization. I haven't tested this, but it's plausible since the problem is forced parameterization.
Per David's second comment, execute the SQL statement dynamically in another database, and reference the original db with 3 part naming. I have confirmed that this works. For example,

exec tempdb.sys.sp_executesql N'select * from TargetDB.dbo.t where json_value(doc, ''$.group_id'') = '''' '