It depends on what you define as combat, though. You can use an incredibly broad definition ('Anyone who is in an active combat zone', or even 'Anyone carrying or managing a weapon') or a very narrow one ('Anyone who can be expected under normal circumstances to come under direct fire'). But even that leaves a large grey area.
If (I'm just talking layman terms here) you're an engineer, your job is not to fight people but to support those who do. But a combat engineer is still quite likely to come indirect or even direct fire, despite fighting not being their primary job. But imagine being in a large-caliber artillery unit. The changes of you coming under direct fire are small, but you are, unlike the engineer, actively trying to kill people. When does your supporting become fighting, and when does your fighting become supporting?
Your social science studies are showing. In the military we prefer clear and defined terminology.
'Anyone who can be expected under normal circumstances to come under direct fire'
This is the usual military definition of combat. Artillerymen wouldn't argue they have seen combat, but nobody would deny their role inside the part of combat.
Combat engineers are classified as fighting units usually because they do not operate in their organic units, rather they get attatched to infantry units.
@olafson another sidenote: dedicated force protection units are not counted as combat units. This does not mean they cannot see combat. The force protection of the Dutch Air Force saw combat frequently considering they also did nearby patrols.
Other soldiers would do it that are equally cappable of fighting on a front line? And they would probably have to fight since supply routes would be attacked and military bases as well?
The thing you are horribly missing is that military =/= combat troops.
The other point is, supply lines do not often get physically attacked by enemy units in a conventional war. More likely they come under artillery or air attack but that does not count as combat.
The reason people nowadays think supply lines get attacked so often is because COIN operation for the past 25 years. In conventional warfare, territory is more defined thus logistics units safer from direct fire.
@bigpete another thing: you are very sadly mistaken in the fact that the military needs psychopaths to do the hardest fighting. This is hilariously far from the point. An anger-based aggressive unit does not perform better in combat than a more balanced unit. Units filled with more intelligent personnel who do not have a sense of bloodlust perform much better in an overall campaign. Why? Every conflict for the past 20 years has been insanely more complicated and they are only getting more complicated. In order to be an effective unit, military personnel need to be able to make sense of what they are doing and they need officers to explain it to them. So no, psychopathic units are not more effective.
I do not want to call them psychopaths, but take the USMC: a unit made to be shock troopers with aggressive conventional-oriented mindset. They do not perform better in combat than Dutch, Norwegian or English units, who are signficantly less aggressive. On the contrary. The USMC has made countless gross judgement calls in Iraq and Afghanistan simply because of the reason not even their higher-ups had any clue of what they were actually DOING.
tl;dr: in order to do your military job well, you need to understand what you're doing in the grand scheme of things. Being mentally unstable has no place in that. They'll make everything into a hammer-and-nail-problem. War is not like that any more.