The obvious benefit of continuing the match into the second day is that it increases the chance of getting a result, given that there is no guarantee that a full day's play is possible on the second day.
Indeed, the 2002 ICC Champions Trophy demonstrated the risk of starting anew. Despite 52 overs being completed on the first day, and 58 on the reserve day, no result was achieved.
This was criticized by experienced former players at the time. Farokh Engineer stated
I think it's absolutely daft. It doesn't make any sense, They should
look at that rule straight away and change it. The obvious thing is to
continue from where they left off.
and Sanjay Manrekar opined
The International Cricket Council should learn a lesson from this
result ahead of the 2003 World Cup. We had more than 100 overs but
still no result. If the match is continued rather than replayed, it
gives you more of a chance to finish the game
Maybe there are other contributing reasons, such as tiredness of a team having to field twice, the unfairness of a team in the ascendancy having to start again, and the odd feeling of important contributions being voided (what if you scored a century, or took a hat-trick?), but the huge benefit is the improved chance of a result being achieved.