広い and 狭い: room size and the range of choices
Compare available space with the range of choices or knowledge, distinguishing spaciousness from general size.
How much space is available
この部屋は広いので、机を二つ置けます。 says that the room is spacious enough for two desks. 広い, read ひろい, focuses on the space available.
廊下が狭いので、荷物を置かないでください。 asks people not to leave luggage in the narrow corridor. 狭い, read せまい, describes limited room, for example for passage.
Compare with 大きい
大きい机を置いたら、部屋が狭く感じられました。 says that the room felt cramped after a large desk was placed in it. It separates the object's size from the remaining space.
幅の広い布を買いました。 says that someone bought wide fabric. It specifies width rather than simultaneously describing length, thickness, or overall size.
The range of choices and knowledge
選択の幅が広いので、自分に合うものを選べます。 says that the range of choices is broad, allowing a suitable choice. It does not concern a physical area.
狭い分野を深く研究しています。 says that someone studies a narrow field in depth. Limited scope does not imply low value.
Does 狭い分野 necessarily mean a field of little value?
Show the answer and why
No. It describes limited scope. Depth and value are separate judgments.