How reasonable would it be for the 1.14 update to have animated waves on water?

Implementing waves via fixed function is a terrible idea. You'd essentially have to retessellate chunk meshes every single frame and waste CPU time calculating wave heights. Instead, you should only upload the chunk mesh once and let the GPU do all the work through a vertex shader; it's the kind of thing GPU's are better at doing than CPU's are. Second, large waves wouldn't look very elegant in the game as-is because you'd see unsightly creases where the triangles for each block meet. You could always use more triangles to render more detail in water blocks, but you risk hurting performance somewhat on lower-end machines depending on the amount of detail.

Heck, I wouldn't even bother displacing vertices to create a wave effect. There are a few other issues you run into when doing simple vertex displacement like: waves could be taller than surrounding blocks creating "holes" where the wave rises above the surrounding blocks, how do you know if the player is underwater when the water surface constantly moves, and interactions between waves and mobs or boats would look really bad if the waves are tall enough without adding some extra complexity to address that.

Instead, I'd argue just a fragment shader + normal maps scrolling over the water surface = good enough, extremely cheap, and you can more easily control the look of the waves; here's an example of such a technique:

/r/Minecraft Thread Parent