The problem is I'd imagine that many who go through the mandatory military service are now indoctrinated and have a bias against the idea of people not having to go through the same they were forced to; something akin to a cultural traditional hazing.

Yes, this is very much the case for many Swiss people. I've often heard "I've been through it, so why should younger generations not go through it too?" and "the military will make boys into real men". Most people also made friendships during military service and experienced good times, so they don't necessarily see it as a bad thing. Just 4 years ago, the people were allowed to directly vote whether we should get rid off conspriction, but 70% voted against it. The Swiss think the tradition of every citizen definding their own country should be upheld.

There is also our conservative government who absolutely loves the military and conscription, naturally they do everything to strengthen it. They fear that the army won't be able to recruit good soldiers anymore if we don't have mandatory service. They also make the alternative (civil service) delibaretely unattractive in order to not lose too many recruits.

However, I'm very lucky that military service in my country is not as harsh as other countries, especially since we're never involved in actual combat.