Space is big. It’s so big that our tiny ape brains have a hard time conceiving of how big it is. The sun is actually (despite it’s size) a relatively small target and is very very far away. Now the more delta-V you burn to slow the trash down the smaller its orbit around the sun will be. But that orbit starts enormous. So to get that purple line near the sun you do need to slow down almost the whole way, just to get it close.