完 puts 元 under a finished roof 宀: the house complete, nothing left to build. Completion drawn as architecture — when the roof is on, the work is 完.
完 ends things: 完成 (accomplish), 吃完 (finish eating), 卖完了 (sold out — the two characters of disappointment at every popular restaurant), 用完 (used up). As a verb-complement it seals any action: V+完 means truly done. And the single dramatic 完了! ('it's over! I'm doomed!') is the national exclamation of realizing you left your phone in the taxi.
Roof 宀 on, house done — FINISHED.
完了 means both 'finished' and 'I'm doomed' — completion and catastrophe, one tone of voice apart.