For those not familiar with moderator messages, see https://meta.stackexchange.com/a/119106/147015:
Sending a mod message (whether suspension is included or not) puts a permanent mark / annotation on the user's account as well as notifies the other moderators on the site and several Stack Exchange employees. Do not use it to respond to the user's flags or for other non-serious issues.
However, there are cases where you really want to inform a user about something but he's not reading e.g. the flag rejection reason or a comment on a post. An example for such a case would be continuous flagging posts in an incorrect but most likely well-meant way.
Right now the possibilities in such a case are limited:
- private email - almost always considered inappropriate
- private message - taints the user's account with a big red "this user has been contacted by a moderator" icon
- chat super-ping - not everyone uses the chat, besides there might be users who don't check their notifications
- public comment - as mentioned above, he might not read it; besides that, responses to flags on a completely unrelated post are kind of off-topic and confusing other people
- declining all their (wrong) flags with the same message - user won't see that unless he checks his flags page
My suggestion is to add a checkbox "Not a serious infraction" when contacting a user via mod message which would not cause the big red icon but a different one. The messages should still be shown in all moderator's notification windows and also be somehow shown when viewing the user's profile as a moderator - just not in the "this user did something bad" way.