This has been a really fun thread to read. Many variables among many variety of DJs with variable skills reaching a variety of goals and ambitions. Geeze, hope that made sense.
Anyway, there seems to be a place where many of us have been or where we want to be. And have settled into a real doable niche.
When I got into this business 40 years ago I experimented with any event, I guess because I hadn't established a preference with so little experience. Because of this I have provided services for probably about every imaginable event style that there is.
And, now because of the vast number of different experiences with so many different styles of music and eras, I can confidently say, I can and will do any event type or ages. And feel equally comfortable at any of them.
A school/teen event one day and a senior citizens party the next, is all good. I'll do either with the same ease.
To answer the OP question, should a DJ be able to do any kind of event? As described by the other who responded, NO. But, is it possible to do any kind of event, YES. if they choose to. I just happen to be one that has chosen to do them all. Never turn down an opportunity.