Lots of reasons why you don’t want to do this.
First, this is a radiant heating stove. Heat radiates in all directions. Hot air rises. Heating capacity or BTU goes by the temperature of each square inch of surface area. You are removing all that square inch surface area of the equation, allowing it to be absorbed into the masonry, instead of heating the house. It’s nice to think of heating the brick and stone mass to radiate the heat into the home, but in actuality, the heat loss to the outside and rising upward out the roof is more heat loss than what moves into the building. (Unless the entire hearth is indoors and extreme high radiating more into the building)
Stoves heat with 2 types of heat. Radiant, as I explained above and Convection. (as explained in the post above) A fireplace Insert has an air chamber around the firebox to move convected hot air out of the firebox with a blower. This hot air is blown into the home making it much more efficient. You want to extract the heat bringing it into the home. The blower will pull cooler air from near the bottom front off the floor around the firebox, and expel it at the top. A stove in an alcove or fireplace opening needs airflow to do that.
Lastly, damage to the stove. Fisher was made of 1/4 inch steel plate, fully welded with a lifetime warranty. Not many are that thick anymore. One of the very few warranty claims was cracking or warping of rear or side sheets when installed in such a manner. As stated above, heat needs to radiate in all directions from the firebox. This also needs to be even. When the back of a stove has little to no airflow, it stays hot in the back, and cools rapidly in the front where it can radiate outward. This temperature differential does not allow even expansion and contraction, breaks welds, cracks or warps sheets. Very bad idea to stress the sheets unequally.
Another reason you have unequal expansion is when a stove is designed with cast iron AND steel plate. The major benefit of cast iron is its ability to move heat. That’s why pans are made of it, and the reason it is difficult to weld. Extreme heat from welding moves away from the weld area so fast, the uneven cooling cracks the iron at, or next to the weld. You have to put the entire piece in an oven or heat with torches, pack in sand as it cools to retain heat and slow cooling. This shows how much heat is removed from the front compared to the back of your stove. You’re making matters worse restricting air flow, and no way should the stove be warranted in an installation of such. It wasn’t designed or tested for that, and you should ask the manufacturer to find if they agree with this.
Also I believe the latest version of NFPA 211 now calls for 18 inches floor protection all around which includes yours in front. If you don’t have that, it’s called a hearth extension to satisfy that requirement.