That’s the best method for identifying the parameter, yes, but it still doesn’t solve your problem. A parameter itself is not read-only. A parameter can be applied to multiple elements and each element determines how that parameter is used and whether it may be read-only or not.
Again, what does it matter if the parameter is read-only or not really? If you can’t modify the parameter then you won’t modify the parameter. Your goal is to update parameter information. You should know what parameter information you’re modifying. You wouldn’t get all parameters from all elements and make blanket changes. You would filter for the specific parameters that you need to modify in the same way that you would filter for the specific elements that need to be updated.