Eriksen plays most of his games wide with Alli playing in that central position. That central position is probably Eriksen's preferred position too and if Alli was missing I think he would get that role over Sigurdsson.
Currently our cover for Eriksen are more natural wide players like Son and Sissoko. Or, if he's not a natural starter when back fit, Lamela. These are the players Sigurdsson would be competing with for game time. Quite like it was when he left, only then it was with Chadli (and Townsend?).
Sigurdsson would in no way provide competition for Alli. He wasn't comfortable wide when he was with us and he hasn't played there for Swansea. He might provide backup for Alli or Eriksen, but I don't think he's better than Son or Lamela. I really struggle to see how he'd get significant game time in his favorite position. You're right, he never got a good run in the side at Spurs in his preferred position. But he didn't get that run because he didn't perform at a high enough level to get that run. Now the competition for that one position he prefers is much tougher. We have one of the most talented young players in the world in that one position.
27 now, 28 in the summer so hardly a young player we can expect to adapt and improve massively either.
Would make very little sense to re-sign him imo.