It's easy to just say they wanted the Stop Watch in the original games simply to have another sub-weapon that could freeze time. Other Konami games of that generation had similar power-ups. Early games didn't need elaborate explanations because that's just how they were. Games weren't focusing on over-reaching plots and story yet.
However, now that we ARE in the 21st century of video gaming, looking back on even past games that didn't intend to have a huge amount of connecting plot points for every little thing, I think it should be something developers and writers retroactively try and explain in the games they make now. It adds something to future games that really can tie an entire continuity together - which personally, would be an awesome achievement and a testament to how dedicated a franchise is about their games.