If you compare the listed wattage of one vs. the other, you may find that the 240V unit has significantly more energy input that must eventually warm everything around it. (Electrical wattage times time equals heat -- in joules convertible to BTU -- search the Internet for the conversion.) Either it heats the air or it heats the cabinet materials. Only by including a higher flow fan to blow room air over the oven body and into the room can more watts be removed without increased heating of the counter and cabinets.

That does make sense as the wattage is significantly higher (1800 vs 7200) I believe, but i don't understand how the minimum mounting height compensates for this. Unless that extra heat is being blown out a lower level that could be hazardous. In that cause I would argue that mounted at counter height is going to discharge that air directly at face level. Not to mention the whole point of a an oven is to keep the energy inside the unit.

Affordable and tolerably thin insulation is not likely in a residential oven. Some heat will conduct outwards where it has to be removed, at least with wood cabinets. My Wolf wall ovens take in air over each of them and push it out below the lower one. You wrote "under the counter," so I would expect the expelled air to be about 24 inches off the floor. This could be a problem for children, but in my experience the air temp is not dangerously hot. But I don't have a GE speed oven to directly address this.

I still don't understand why other brands allow their 240v appliances mounted under counter?

Without having complete design information on these "other brands," it is not possible to do more than speculate on where in the trade-space they might have selected their power input, insulation, and cooling performance.

I'm pretty sure the restriction with the GE 220v has to do with heat dissipation as a result of its ability to use the high power halogen light as well as another heating element at the same time during speed cooking. The 120v can only run 1 heat source at a time so it switches back and forth. I think the constant heat from the halogen must be a driving factor that potentially causes it to radiate more than the 120v. What i can't understand is why it's ok for wood cabinets and shelving to be be directly above and below the unit but a countertop is not. I believe it's because a laminate countertop would not fair well with the heat however I assume most people spending almost $4k for this oven/microwave are using some sort of stone or synthetic material.

If the specific concern is for countertop material, then (ideally) GE should have been more detailed in their limitations. For example, granite can probably handle up to boiling point of water or higher depending on its porosity and moisture content. Higher temperatures may cause internal steam formation leading to spalling. Soapstone can handle much higher temperatures (1000C) up to the point where it converts to enstatite, an electrical ceramic like insulator. Corian and "quartz" countertops are not stone, and are easily scorched or softened at oven vent temperatures. (See quartz back splash threads here.)

I recommend soapstone wherever above boiling point pots, pans, or trays may be placed directly on the surface.