When exporting from Illustrator ensure Advanced Options > CSS Properties are set to Presentation Attributes

Issues
... but you will deal with much bigger problem - "holes" in segments. This is partly because of blender's issue (for years) to handle right points on the same Z axis (I guess) ... partly because of bad topology (double points or screwed path). I don't know about any better solution than take care manually piece by piece to check the problematic place.

Another issue is overlapping parts that seems to be an another issue called Z-fight ... since blender reads all these elements at the same level there is not clear what to render bellow and what is above ... so you can expect artefacts in render (or even visible in viewport) or already hidden parts of railing.
Tip
I don't know what is your goal, but to avoid all these issues consider to Import SVG as Grease Pencil object that supports layers.