Crystal shape is a design decision, not a spec-sheet upgrade. A domed crystal does something specific to how a dial reads, and it costs you something in return.
What a dome actually does
It bends light at the edges. Look at a domed crystal from an angle and the outer edge of the dial distorts slightly, curving away from you — the same effect as looking through a shallow lens. On a plain dial that just reads as warmth. On a raised or textured dial it reads as depth, because the glass curve and the dial curve reinforce each other.
That is why watches built around a three-dimensional dial nearly always dome the crystal. Put flat glass over a domed dial and you get a hard reflective band straight across the middle of it — the two surfaces are fighting.
What it costs
Height, mostly. A dome adds one to three millimetres above the bezel, which is one to three millimetres further from your wrist and one more thing to catch on a doorframe. It also picks up more stray reflection at the edges unless the underside is coated.
When flat is the right answer
Thin dress watches, anything meant to slide under a cuff, and dials that are already high-contrast and flat. A dome on a plain black three-hander adds nothing but height.
Box, double-dome, single-dome — does the name matter?
A little. A box crystal has flat sides and a flat top, sitting proud like a block — vintage look, heavy distortion at the edge. A single dome curves on top only. A double dome curves on both faces, which cancels most of the distortion while keeping the shape; it is the most expensive to make and the one you want if you dislike the fishbowl effect.
The PINDU P6676 uses a curved crystal over a raised planet dial for exactly the reason above — the review goes into how it behaves in practice, and the crystal materials guide covers what it is made of.