I often say that talking of something approaching infinity is meaningless; but doesn’t the same apply to the speed of light?

Something that travels at c has an absolute speed. It remains the same irrespective of the speed of anything around it.

Something that travels at subluminal speed has no absolute speed, it's all relative.

Is the complication of changing from relative motion to absolute motion another reason why it is not possible to accelerate from one to the other?

There never was nothing.