The size of the focal spot is one of the two factors who dominate the detail visibility of a system.
Having a focal spot with nearly no dimension (perfect point), there would be no influence on the unsharpness due to the focal spot:

The edge of the object would be razar sharp and the flaw woould have a strong signal.
But in practice all focal spots have a 2D dimension - even the so called "nano-focus" tubes. If we take the same picture as above and now have a real size of the focal spot we will see that the sharp edge of the object is smeared with the unsharpness Ug. The signal of the flaw in much lower - but is in integrated over the area the same:

Without noise in the image this would be not a big issue, but there is no X-ray image without noise. The task is to asure that the flaws which you have to detect have higher signal level compared to the noise level in the image. The following diagram is taken from the topice in the image quality sector:


The details of unsharpness due to the foacl spot is described in the thread

Why not always take a very small focal spot?
The physics of a X-ray tube set the limits.

Only 2% of the energy is transformed to X-ray quants, about 98% is heat, which will be on the small focal spot. The target (anode) where the electron beam is focused to is mainly made of tungsten due to the high melting point (3,422 °C). Tungsten is not a good heat transmitter, therefore it is embetted in copper, which could transfer the heat much better. Here is apicture of a tungsten target in cooper, destroyed by heat:

The copper itself is cooled with flowing water to bring the energy to somewhere else.
The energy density of the focal spot is about 1000W per square mm with a target of 20°. If the target is steeper, the size of the tungsten is larger; at 11° about 1800W can be used with such a tube. (hint: with 1mm*1mm focal spot size a 45° target would have the dimension of 1mm*1,17mm, a 20° target already has 1mm*3mm and a 11° target 1mm*5.7mm and the larger size could transfer more heat).

More power produces more dose. A higher dose rate lead faster to the image or give less noise in the image. The detail visibility also depends on noise, as shown in the thread .

My favorit image to show the difference is the BAM5 weld:




Finally it is a trade off in the triangle between high dose or high spatial resolution or fast image capture - which is the content of the thread .