The answer has something to do with PRESSURE.
We know that Pressure is directly proportional to Force applied and inversely proportional to the area of contact.
This means that when we increase the area, less pressure is exerted. And when we decrease area, more pressure is exerted.
When the handle of a suitcase is narrow, this means that the area of contact between our hand and the suitcase is narrow. The force acting is gravity. As the area of contact is less, more pressure is exerted on our hand, just like a knife would do. So, we may feel pain and difficulty in lifting the bag.
So, to decrease strain on our hand, we decrease pressure by increasing area of contact. We do this by increasing the surface area of the handle, i.e. we use a broad and thick handle.
As the broad and thick handle increases the surface area, less pressure is exerted on our hand and it is easy for us to lift it. Moreover, we get a better grip.
Thus, broad and thick handles are preferred in suitcases.