So the reason Christians don't even have ministry on their list is because what Christians care about is money, status, fame? If so, that's sad.
I can understand why NON-CHRISTIANS would not even consider Christian ministry at all.... but Christians?
From what I can gather many people in full-time ministry wouldn't recommend it as a career choice. For me it's one of many life choices that I'd look to discourage people from exploring. The ones who are sufficiently easily discouraged that they would choose something else because a couple of people said it was a long uphill road with little respite are probably the ones who would struggle and quit when they realised it was a long uphill road with little respite.
Even from a purely Christian perspective, it's not for me to suggest to a class that some of them might consider Christian ministry. I might suggest to an individual that I could see how God might be calling on them to consider such a thing but even then I wouldn't specifically recommend they do it, just that they consider whether God is calling them. If someone is brilliant at nuclear physics it makes sense to suggest they consider a career as a nuclear physicist because it's a career rather than a calling. If someone is an amazing Bible scholar it doesn't necessarily mean they will be a good pastor. If someone is very good with people and very caring it doesn't necessarily mean they will be a good pastor. If God is calling them to be a pastor it doesn't matter if they don't seem like they'd be very good at the job - just look at Moses.
As I understand it, over half a century ago when Catholics (at least) still considered ministry as a viable vocation (worth putting on the list of possibilities, anyway) it was often put into the context of the story of Eli and Samuel. NOT to suggest someone welcome this vocation WITHOUT being Called but rather BECAUSE he is being Called. Samuel didn't know what was happening.... Eli lead him to see the voice of God.
But yeah.... if Christian parents, Sunday School teachers, Youth workers, pastors only consider options that are abundant in money, power, fame and status - then perhaps they'd only discuss other things. And that may well be why Christian ministry just isn't on the radar anymore. And why we see a severe shortage of pastors in many denominations (including mine). Interesting, because it applies to ME, too. NO ONE EVER even brought up as a theoretical possibly being a pastor.... and I never considered that possibility. Doctor, lawyer, zillionaire businessman were usually the things promoted by parents, relatives, friends, teachers.... I think something might be amiss here. Could it be that Samuels today never "hear" a Call because it's just totally off their radar? Or maybe (worse) because Christian ministry is discouraged, frowned on, because they may lack wealth, power and fame?
I'd suggest the solution is to make sure people are available, and known to be available, to discuss a potential calling. I would see two potential situations that are highly undesirable here - one is people constantly thinking they are "hearing God's call" just because someone put a bug in their ear regarding what it might look like so they are endlessly looking for things that might tick boxes. The other is people hearing the call but having no idea who to talk to about it, or assuming they must be imagining it (or, worse, assuming something is wrong with them because nobody should be hearing voices).
Some time back I met with my pastor and introduced what I wanted with a line "either my imagination is in overdrive or God is calling me to do something very unusual". It certainly piqued his interest, and we talked over a number of signs that seemed to be aligning and pointing the same way for me, with a view to determining whether this really was God's leading or I'd just got an idea in my head and nothing more. There was precisely nothing he could have done ahead of time to point me in the way we concluded God was leading, all I needed from him was knowing he was available to talk things over and help me draw a conclusion. Had he been of the opinion that I would make a good pastor there's no reason why he shouldn't have asked if I could meet with him, explained what led him to his conclusion, and urged me to prayerfully consider it.
To the casual observer my pastor has a pretty easy life. He's in the church office four mornings a week and obviously in church on a Sunday morning. That's a pretty cushy number, when you're drawing a full-time salary, right? Except of course the casual observer doesn't see the amount of time he spends on things other than visibly Being At Church. Like when a church member dies and he spends time with the family, or when (like above) someone comes to him for advice regarding a possible call and he may end up meeting with them regularly for an extended period. Or the number of meetings he attends in the evenings, because church volunteers who sit on committees typically have full-time jobs. Or the times people openly express dissatisfaction with him, when he's working harder than ever. Or the fact that, as the pastor, he's the one people go to for help and support but he doesn't have any obvious people to go to when he needs help and support, and as the leader of the church he's the first into the (spiritual) battle so presumably takes the brunt of that too. My former pastor once told me that among the hardest aspects of the job was holding someone's entire life in your hands and having to pick up someone's world and put it down because today you might be with a family that is grieving the loss of a loved one, tomorrow you're with a young couple who just got engaged and want to plan their wedding, and the next day you'll be with another couple who are desperate for a child but just miscarried for the seventh time. The last thing any church needs is the kind of person who heard the idea that they might be a pastor, looks at the visible work the pastor does and figures it's an easy ride, and jumps in expecting it to be easy.