How often has it happened to you?
A decent idea that might be workable. Front and center. You think about writing it down but trust yourself that it will be so good that you will recall it later. Only when you recall later, you just recall that you had a seemingly brilliant thought that vanished. Gone completely.
Inspired ideas cannot be left lost. Whether they become something worthwhile down the road, or something that gets shelved. Why take that chance? Keep paper close by. Most dollar stores sell small notebooks and pens for cheap. So stock up and place them wherever in your home you might most frequent. Just knowing you can reach for a place to write something down can put your creative mind at slight ease.
If you have a smart phone, you have an extra note-booking device on you at all times. Anyone with an iPhone can easily tap out an idea on to notes for transcription later. If you have dictation enabled on your phone, you can verbalize that thought directly on to the notes application. On occasion, I have used Voice Memos to dictate something and expand on it just so I can remind myself of any extra things in connection with the idea.
Even with the assistance of technology, I still think it is vital to keep paper around. Ultimately you will do whatever is best for your writing practice. For me personally and professionally, having both options available is makes it a seem like writing insurance policy for ideas.
It is minimizing the potential for loss of potentially brilliant writing. Something that may seem insignificant at first can be revisited later with a fresh mind and fresher approach. It could be the premise to an eventual best-selling book, a highly-read and trafficked blog post. Anything. So why risk losing those creative sparks? Give them the imprint and guarantee they stand a chance at existence and eventual development.