I personally believe the chance of Google/Apple/Microsoft adding MDM API's for any third-party MDM solution to delete all SMS messages on enterprise devices of their corresponding platform is extremely small.    You probably need to find/buy/build a third-party SMS reader app with capability to delete SMS messages when receiving  request via the the industry-standard AppConfig framework.   I really don't know if such app already exists or not.  However,  If my company find a good enough profit margin and big enough market size, we could consider working on such B2B apps.  

What if I try manually? Using the option "Wipe program data" on each device? On applications tab. Which android app is storing the messages?

Messages - com.android.mms

Phone/Messaging Storage - com.android.providers.telephony

Or some other?

If you are ready to take risk and make THOROUGH tests on your devices, you can decide YOURSELF whether to proceed with remaining production devices based on your OWN test results.  Personally, my gut feeling tells me it is not likely to work except under very special circumstances.

I can think of a few issues with your proposed approach:

1. Depending on your MobiControl server version, Android device agent version, device firmware version and device enrollment mode, the "wipe program data" action/script may not work at all for any apps.

2. Even if the action/script command works,  performing such operation will remove ALL application data consumed by the targeted app.  Unless you have carefully tested and confirmed the operation does not remove other important data on your production devices, you risk losing such data, which might be critital to your device end-user or your business operation.

3. SMS messages are generally stored in the system SMS database for shared access by the device default messaging app (e.g. com.android.mms for many Android devices) and possibly other third-party messaging apps installed on your devices.  To avoid undesirable side-effect(s) to other apps accessing the shared SMS database, it is safer that any operation removing individual SMS message is well-defined and targeted precisely, rather than a single action to to remove all data associated with a messaging app.