Neither budget impact nor simple duration should be the only criteria to judge a trip.
Here in Japan, I have seen people do two-week stays that only scratched the surface, while others, in a week, experienced a deeper immersion by focusing on a cultural niche.
You can ignore the binary menu "long and cheap" or "short and expensive" and prioritize a rich experience.
For example, a one-week trip dedicated to studying the ceramics of Kyoto or local cuisine can be more "cost-effective" in terms of experience than a month of ticking off tourist sites without truly understanding.
You should look for the third way of depth, not just length.