You get more free gearing with the hydrostat, and much smaller package and less weight. Take a 60hp diesel and hook it to a hydraulic drive servo. It makes up to 4500 psi peak pressure, or 8 gpm peak flow. It gives infinite gearing from max reverse to max forward speed. The servo weighs about 30 pounds and is the size of a loaf of bread. The wheel motors are the size of a coffee mug and sit inside an axle tube. They might have a vol/rev that is ten times or more greater than the servo, giving 2X10 = 20:1 mechanical reduction. There is no torque differential with speed differential when turning unless you build this in (which you normally do in bigger machines). You can drive as many wheels as you like with relative ease (just some plumbing and a block with some check valves). So there is a huge savings in getting rid of mechanical multispeed transmissions. (Some equipment will still have road gears - a mechanical tranny between the engine and servo).
Hydrostats make a lot of heat, but they carry it all away in the return line to a fluid cooler. E-motors don't have this feature. You would need a sealed motor with liquid cooling circuit to fit it in an axle tube.
Hydrostats have most of the control computer executed as plumbing hardware. This can be good or bad. You don't need an electrical genius to troubleshoot the system. You do need a trained hydraulics tech.
So show me the engine/genny/electric motor combo you had in mind that can match the maximum torque capability of a hydrostat system set at 4500 psi with a 20:1 vol/turn ratio from servo to wheels. Or at lease one that can spin all four wheels of a machine on dry concrete, and still perform at speed. In other words, calculate the flow rate of 4500 psi at 60 hp. And calculate the pressure at 8 gpm and 60 hp, and try to duplicate that sort of versatility with an electric motor controller that can be pressure washed twice per day for 20 years.
The biggest downside by far is that leaking hydraulic fluid kills grass better than glyphosate.
For zero turns, its pretty much the same. You need two servos with separate actuators. But you can still get 1000:1 direct reduction from the hydrostats. Often, the transport function is sort of a pto load, with the deck drive hooked (belted) to the engine shaft mechanically. So if you hang a genset off the crankshaft, you need to figure out how you will drive the deck.
This isn't to say electrics are bad. The lunar rover went with electrics, but it wasn't mowing grass; and it had some pretty fancy hub reducers that probably wouldn't hold up too well where I work.