would they not all trace back to a common word?

Well, it's hard to reconstruct words in PIE. What's usually being done is reconstructing roots. A lot of work needs to be done on the morphology and grammar of PIE. But above in one of my posts, I said that porta 'gate', portus 'port', and the -port verbs all trace back to a PIE root.

Ceci n'est pas un seing.