Hi Keshab;
That is called a brick bell, it has become a very common design.
You are correct in that it will hold heat longer.
It also will take quite a bit longer to heat up.
The barrel's purpose is to provide instant radiant heat. If your
RMH is kept warm all winter long, then you will not miss that radiant heat.
However, during spring and fall, you might wish you had some radiant heat rather than waiting several hours for your brickwork to warm up.
After it has warmed up, you may find it is now way too hot indoors.
You can build a brick bell and then place a steel plate above the riser.
This will give you quick radiant heat and a spot to set a kettle but will have much less surface area than a barrel.
An
RMH is not burned like a conventional
wood stove.
In an insulated home, you do not need or want your RMH burning non-stop.
A fire in the morning and another in the evening is the only time your stove is lit, the rest of the time it sits there releasing all the heat you just added.