Basically, you build Spirit Visage and Sheen for laning phase. Then, you complete Iceborn Gauntlet before you begin grouping (or splitpushing against an AD champion). If you don't have armor in the mid-game, you'll just be melted down by the enemy ADC or AD fighters.
While building Spirit Visage into Trinity Force would help against an AP opponent, you'd lack the armor you need to survive in mid-game skirmishes and teamfights.
While you could build a dedicated armor item before finishing Trinity Force, it would delay your powerspike. Also, you'd either overcap CDR (TF, FH, SV = 50% CDR) or you'd spend most of the game with uncapped CDR (i.e. if you build RO or Thornmail instead of FH).
There is the option of building Spirit Visage + Sheen + Warden's Mail/Chain Vest before completing Trinity Force, but you'll still be missing 10% CDR for a significant portion of the game. Spirit Visage + Sheen + Glacial Shroud would resolve the lack of CDR, but it doesn't provide much in the way of armor.