I really don't like the Morale rules and don't use them, but the players have been good about responding to morale related issues, taking shore leaves, letting the scientists collect data etc. Then again, they've always had a place to resupply and take shore leave, since they haven't left Charted Space yet, so they probably wouldn't have run up against any morale problems. (They've been in Charted Space for about 1 1/2 years now, which is fine since why gloss over the adventure you have a map for just to get to the adventure you don't have a map for?) They've had to cope with plenty of HR problems in their crew, but I've limited the ones we give game time to, to interesting problems, since boring ones would just be handled with Admin, Leadership or Advocate roles and I assume those work out as "an NPC you don't know and don't care about gets fired, and gets replaced by another NPC you also don't know and also don't care about". So, just tell them this is assumed to be happening in Charted Space, its part of your job, but will drop off the further you get from the Imperium. After a while, lose people and and it reflects in attrition, and mostly no one will leave since there is no where to go.
I may change my mind and try to use the mechanics later, since the situation will change, but for now I'm trying to take a show, don't tell approach to Morale, and make those related to specific kinds of events, about which they PCs could have done something but in some cases didn't - like psychedelic drugs being easily available on one planet, loose hiring practices around background checks, religious divisions, desire of many crew to do something against the Zhodani or Zydarans. Of course, these are all dilemmas - do one thing and you solve the problem one way but end up with a different problem.