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It might take more delta v but it would be worth it
Been a while since my Kerbal days when I read a bit about all this orbital mechanics crap and I remember that there was something counterintuitive about the delta-v required to hit the sun vs escape the solar system; I think compared to escaping, if you start from Earth you need almost 3x the delta-v to hit the sun, but I can't remember why. Something to do with the huge gravity well, because it got worse the closer you are to the sun
edit: lol I totally misread you, but also I found a video and duh yeah the reason was obvious: it's because we're moving around the sun at ~30km/s and to hit the sun you need to use that much delta-v to slow down to make your orbit tight enough to actually hit the sun instead of getting slingshotted / staying in orbit: https://youtu.be/LHvR1fRTW8g?si=1eIyeeqWR61wRu08. Escape velocity for the solar system is ~10km/s