And this is where we differ - I think _your_ opinion is outdated ;) The services that you listed mostly do not require an "army", what exactly is camouflage gear & combat training good for with regards to helping with covid-related tasks (or any other "Katastrophenhilfe"-related endeavour)?
The "Swiss army knife" metaphor is exactly what I so despise about the Swiss army; it's their excuse for essentially being an eternal "Pfadilager" for adults. Actual participation in conflicts mentioned by GP aren't an option anyway thanks to Switzerland's neutrality.
Luckily, it seems the trend is clearly in my opinion's favor, as was evident once again with the results of the last referendum on fighter jets - the pro-army-folks are a dying breed, it is just a matter of time until the 'Wehrpflicht' is finally abolished (I estimate it takes another ~20 years or so until the cold war era generation starts to become a minority), and when that happens, it's just a matter of time until the rest of the army gets to boot too, as all the nostalgia-driven sentiments towards it will not exist anymore (currently, put 10 Swiss men in a room, and it will take at most half an hour until their army experience becomes a topic).
And you know what? It'll be for the better of the world, and Switzerland especially. Finally, we will be able to say "We do not participate in this barbarian head smashing anymore, we're civilized folks"; someone needs to make the start and Switzerland is in the best position to do so. We're already not participating anyway; but we're still training generation after generation to do so; and this needs to stop eventually. My hope is that this will be the case in the next 20-30 years or so, I wouldn't mind if it was earlier ;)