DAI being open world is likely a direct result of the massive number of complaints about DA2's linearity.
Origins also wasn't open world. Didn't hurt it much. Bioware adjusting for Inquisition is mainly the result of Bioware checking what's most popular, and adjusting accordingly. E.g. chasing market trends. As it's always been (even before EA). The only ever exception from that was arguably Origins -- meant to be a throwback and "back to the roots" to Baldur's Gate, including it's more tactical form of party-based combat.
BioWare hasn't turned a deaf ear to the criticisms players had for Dragon Age II. In a recent interview, BioWare's CEO Dr. Ray Muzyka stated that in addition to addressing those problems in the next Dragon Age, the studio is also drawing inspiration from other popular titles on the market, including Bethesda's dominating RPG, Skyrim.
Skyrim was the biggest kid on the gaming block when they sat down for Inquisition. That's it.
