I have imported an SVG into Inkscape but I have this weird "pinching" behavior where the stroke is thinner at the top of the curve where the point density is higher. Is this normal and how can I prevent it?

I'd try ungrouping the object. 

There is also a setting for transforms in the Preferences dialog that can be set to optimize, instead of preserve. 

There could also be a path effect on the object. Selecting the object will display information in the status bar at the bottom of the screen

It's definitely a bug. None of the suggestions applied in my case. I tried moving the object around and the width automagically adjusted and now I have a nice curve. Thanks anyway!

Probably not a bug. More likely the imported object had a transform and it was optimized when the object was moved. Inkscape will not rewrite an object in the xml until it the object is moved.

Here is the file so you can take a look for yourself.

As noted above the object has a transform applied, truncating the stroke . When moving the object the transform is removed and the stroke is restored (provided the settings are optimized).

This stroke variation is expected behavior. It can be reproduced by grouping before transforming, or keeping the transforms preserved.

Thank you for your answer, now I understand where the problem came from.