So our preferences and suggestions are extremely diluted, and Bethesda will do whatever its business managers believe will sell the most copies, which may or may not include a change of game engine.
Bethesda will choose the engine that lets them best do what they want, balanced by its cost. Normally I'd exclude that last point, I imagine most of the AAA engines are fairly comparable when it comes to their price. However now that id and Bethesda are both Zenimax Media companies it probably is a factor worth considering.
Although this is less true now, certainly when Morrowind was in developement few games combined a large open world with such high object detail. TES III didn't have the absolutely best graphics of its time, but the fact that almost all objects were individual items, and that the game world was so large and open, was a nearly unique combination.
Given the unique needs of the developers Gamebyro (then NetImmerse) was a very appealing game engine because it was extremely customizable. In fact it was specifically designed to be customized and added to. I think it's less true now, but at the time is was basically just a graphics engine, and the other aspects were minimized so the developer could mold the engine to their specific needs. An extreme range of games ran on NetImmerse: RPGs, FPSs, RTSs, sims, and even MMOs. Compare this to the Unreal engine, where most games don't stray too far from its first person/third person origins.
Today I think most game engines are specifically built to handle both large open areas and high object detail, so Bethesda has far more choice when it comes to achieving this balance. Now, if they're still looking for something very customizable, or very familiar, Gamebyro may be their best bet. However I
expect they could do what they want with most of these engines, and of course id tech 5 likely has the more appealing price tag.
But, as I mentioned before, we need to be careful about considering what Bethesda
will do some of it may have started some time ago.