This is true of the current model, although the core team was receptive to the idea of changing this in their feedback to SE-0018. If it were changed, the model would be "immutable after initialization". Assignment in the declaration would be treated as a default initialization that is not used if an initializer provides a different value for the constant.
I understand that you want to keep this proposal simple so I think it's ok to leave that enhancement off for now, but supporting this is a viable future direction.
As the author of SE-0018, I would really like to revisit the topic in a more comprehensive manner someday, but I think this is a good intermediate step that would not conflict with any direction we might eventually take. It fills an obvious gap in the current initializer synthesis and should be straightforward to implement.