Detail View - Search every fields and not only the Display Column Field

I also agree, although what I usually do is construct a Display Value column out of all important pieces of data, not just designate one of the data columns (e.g. Full Name or Product ID). This way I have a helpful summary of information wherever that row is referenced, no matter the context:

This makes it more searchable, but also takes quite a bit extra of doc space (a longer string is not only stored for each row, but also for every reference when it’s displayed.) So balance is required there, and converting that to plain text is also a must.