Key part being "for military purposes". To me it is bizarre that these apps were being used in the first place. Does a national military really not have better/more secure ways to communicate internally than off-the-shelf messaging apps?
Source: https://en.wikipedia.org/wiki/Conscription_in_Switzerland
You get your orders for your once a year repetition course about 3 months before, then show them to your HR department, who arranges for you to have paid time off, paid by the unemployment insurance or something. Then you go do it and come back to work. Your colleagues pick up your tasks while you are gone because you'll do the same for them later (and good teams value cross training anyway). Source: I was a team lead on a team with active Swiss army soldiers.
While you are doing exercises, you have access to all the normal army comms stuff, including presumably encrypted digital HF radio for voice and data, satellite days, VHF radios, etc.
This order is saying, "don't use commercial products, use the military comms systems we give you".
Kind of too bad they didn't give an exception for Signal though... :)
Especially if in response to some claimed attack on the public logs the company would say, "hah, hah, JK, the stream has been xor'd with /dev/random all along anyway".
A few years back, US bases could be spotted using a fitness trackers heat map: https://www.theguardian.com/world/2018/jan/28/fitness-tracki...
Whereas these would never (usually) be used 'in the field'
For example, to an adversary able to see the direct one to one social messages between a platoon of soldiers can probably easily figure out social dynamics, who might be most easily bribed, etc.
Hence why they put a limit on the usable chat systems.
The worry also should extend to private conversations between to military members.
But you can't really or them all the time to use military controlled apps, that in practice just doesn't work out. So limiting them to commercial but reasonable secure solutions which are under a local jurisdiction is a reasonable good solution.
A public accessible Swiss military payed Signal fork probably would be an better solution tbh., but Threema isn't bad either. Just not quite as good as Signal.
You don't want people to get into bad habits.
By military purposes they probably don't mean to message buddies to break the door during an operation, for this they will use proper military gear. However you can imagine military personel discussing military stuff on WhatsApp etc. Stuff like scheduling things, clarifying information, discussing classified stuff to form an opinion or make a decision.
Some of the better of the shelf apps are as or more secure then many of the military internal developed solutions of many militaries. At lest when applied to use-cases outside of war zones and similar.
I mean there are top of the line security experts all around the world directly and indirectly contributing to apps like Signal. On the other hand the amount of scrutiny a proprietary military app will receive is limited.
But more important "for military purposes" includes a lot of situations you might not have considered.
Like more or less all communication done between two active members of the military, even if of duty, as long as work content might pop up in the conversation.
Or like they sending a member on break a message that due to weather forecast there is a good chance they will have to interrupt your brake for helping with "disaster relive" (which can e.g. include removing snow after some unusual heavy snow fall, or helping with cleanup after a avalanche). To just name some situations.
Their annual defense budget is $5B+.
"Switzerland to Spend $2.5 Billion in Military Upgrades" (https://www.thedefensepost.com/2021/06/15/switzerland-invest...). Just last year they allocated $284 million towards "command and communication systems". You can build a hundred Whatsapps from scratch with that money. Where exactly did it all go?
On hardened physical crypto radios I presume - rather than on consumer-grade apps.