There is no problem with it, but I assume there are many people who will look upon you favourably if they think you do a highly skilled job. While many of us may not care to impress those people, there are certainly those who do (possibly people with similar attitudes who care more about validation from people who think like them)
But we should also acknowledge that there's an entire culture built around valuing people and their time relative to one's perception of their "importance", that this culture can influence one's earning potential and acquisition of material possessions, and that many people do care about things like "seeming important" or moving upwards in this hierarchy as a result.
I think which direction you choose is about knowing your audience. As you mentioned, different people value different things and humans often want to present a different view of ourselves to different people at different times.
A somewhat ungenerous characterization of the attitude may be something like the Rocket Scientist vs Brain Surgeon sketch - https://www.youtube.com/watch?v=THNPmhBl-8I
But we should also acknowledge that there's an entire culture built around valuing people and their time relative to one's perception of their "importance", that this culture can influence one's earning potential and acquisition of material possessions, and that many people do care about things like "seeming important" or moving upwards in this hierarchy as a result.