Yes, they should always make clear via what the Doctor says and what the companion expresses during their time, that travelling with the Doctor is playing with fire, its dangerous but the wonder of travelling through time and space makes the companion take the risk...
People on Earth now, including me, would love to go up to space, to the moon or the international space station, and in doing so would be putting our lives at risk like our astronauts do but that's a choice we'd gladly make... we have seen how it can go wrong, and people have died just trying to get up there.
They are doing it to experience something awe inspiring and unique, something so few will experience, and that's just to float about the immediate space above our planet and nothing else.
Imagine how striking the prospect would be of travelling with the Doctor.. going through time and space, walking on a ground that's not Earth's, breathing in the air of another world, visiting days long gone.. it would be mind blowing and extraordinary, it makes perfect sense that someone would risk their life to experience the wonder of it all, but it should be noted, that's what the companion is doing by living this life, and they should wrestle with that and not be fully ok with it but ultimately the lure of time and space is to strong to amazing so they go (or continue) on the adventures.
Now a way to write a companion out could be something real bad happens and they say enough, draw the line here I'm not risking my life any further.. and so on, an experience that shakes them and makes the reality of the danger now out weigh the wonder of travelling.
One of the ways DW as a program fails in my opinion is that it never fully explores or lives up to the idea that a companion is playing with fire and this can and will (eventually at some point) have a bad end (although the end of the god complex was good at playing with this I thought) I'd like to see some of the companions die, not all of them obviously that would be to morbid but some should stop travelling, some could get lost (rose) and some should die... and none of this but she lives on rubbish that we got with Clara, that's a cop-out, a proper done and done bang your dead death... It fully represents the dangers of the Doctor and his way of life in the Tardis... but I think the show plays to safe to ever adopt such a approach, unfortunately.