What are the advantages and disadvantages of one versus two plies?
For controlled impedance, you get the best performance with zero plies. That is, if you are concerned about a repeatable RF performance between certain layers in a multilayer PCB layup, you should arrange for the impedance critical layers to be separated by core.
If pre-preg between signal and ground is unavaoidable, then arrange for that space to be mostly core, and minimise the pre-preg thickness, so the core dominates the gap.
In your case with inner planes and tracks on the outer layers, it sounds like the PCB fab is trying to sell you a foil-prepreg-core-prepreg-foil arrangement. Ask for a core-prepreg-core quotation. It might be slightly more expensive, but the inner to outer impedance will be better controlled.
If you want the board to be built at any one of several fabs, or are prototyping at one fab then building in volume at another, then it's vital that your controlled impedance layers use core. Because core is built and supplied to a specification, you can control what the fab uses. Even if you specify the pre-preg material, each fab may handle, assemble, press and cure it differently, and even the same fab may do those differently at different times. Using pre-preg for controlled impedance layers is a good way to get unexplained variations in performance between builds.
Most PCB stack-up I have seen use two plies for prepreg layers, even if the same thickness could be accomplished with a single, thicker ply. Why is that?
It's mostly down to the economics of the FAB. I've they've got a good deal on the thin stuff, then they'll use it in preference to the thick. One or two plies, pre-preg is bad for consistency.
In theory, two plies of pre-preg will give you better (less bad) dk isotropy if they are at 45 degrees to each other. Are the fab offering this orientation option, even if at a higher price? Obviously it wastes material for them, and will compromise their standard handling.
You don't say what frequency you're operating at or what tolerance you want to achieve. FR4, core or pre-preg, by the electrical loss of the resin, the coarseness of the glass weave, and the variability of the glass/resin proportions, performs poorly above a few hundred MHz. But core is less bad, it has a much better dimensional and dielectric constant tolerance than pre-preg. Core is made under repeatable conditions, whereas pre-preg is pressed between whatever copper etching you happen to have done.
Remarkably, FR4 is used in WiFi to 2.4GHz, where the designers have used a lot of skill to make the circuit accept the poor tolerance and loss, for the cost benefits. If you are working at 2.4GHz, then using pre-preg rather than core for your FR4 layers is one risk too far.
If you want high tolerance, or are operating in the GHz, then you might want to consider RO4350 for the outer cores, with FR4 pre-preg to join them together. It's more expensive than FR4, but an order of magnitude better on RF tolerance, and better yet on performance. It's compatible with FR4 processing, so can be assembled the same way.