I appreciate your frustration but its just a case of knowing the software and the terminology used within it.
A 'Path' technically cannot be 'rasterized' in the true sense of the word, a path being just that, a path, along which you can then do something....paint, erase, blur, sharpen etc etc.
For example, with a path selected, and on a new blank layer, you could 'Paint' along that path with the current 'Brush' tool.
Likewise, you could use the 'Path' for a 'Blur' operation....this would affect the currently selected layer....there needs to be pixels on the layer in order for them to be 'blurred'.
'Rasterizing', as defined by PS, a path is not just a simple case of having a 'rasterize' option.....what is there to rasterize?
Instead, you use the 'Path' to apply a 'Raster' effect along that path, be that painting with the 'Brush' tool on a new layer or 'Blurring' an existing image layer.
This gives you enormous flexibility in the 'style' of the result, the options for the 'Brush' tool tool alone are vast.
Now, having said all that there are two downsides...
1. You need to set up whatever 'tool' you are going to use before applying it to a 'Path'.
2. Each time you apply a 'Raster' effect it becomes permanent, non-editable, or 'Rasterized'. Editing the 'Path' afterwards will not change the previous result, it just edits the 'Path' ready for the next 'Raster' effect you want to do.
In order to be able to 'Edit' a stroked 'Path' after the effect you need to create an 'Open' 'Shape'.
This will have both 'Fill' and 'Stroke' properties which can be changed at a later date.....a 'Shape' being more like an individual object rather than just defining a 'route' along which to do stuff.
'Shapes' can be edited in just the same way as paths but will also 'update' their 'stroke' and 'Fill' properties at the same time. 'Shapes' are 'Rasterized' by consciously choosing to do so or by saving out to a normal image file...jpg, png, bmp etc etc.
As a rule of thumb 'Paths' define a route along which a 'Raster' effect can happen on the layer selected.
'Shapes' have their own layer, can be 'Filled' and 'Stroked' and remain a 'vector' until 'Rasterized'.
Regards.
MrToM.