...which would then likely void the warranty on the new vinyl window that you installed, and potentially cause damage to it if heat builds up enough on a hot sunny day. Reflections from low-e coatings have melted vinyl siding on neighboring neighboring homes given the proper circumstances, they could most certainly heat up air trapped inside of that storm enough to deform the vinyl.
Nothing wrong with using storm windows when appropriate, they can add to energy efficiency, just not recommended with vinyl replacement windows.

Thanks for the tip, glad I mentioned it. Perhaps exactly why I have never seen anyone talk of putting storms on vinyl. That may answer my question, why don't vinyl window people make vinyl storm windows? Next time shopping, I'll "curiously inquire" with the salesman about doing such a thing, and see what the repsonse is. Would be nice to hear from any amateurs (like me) who may have done this, and what happened.

Love the ad but you do need to be careful about what Karateguy says.

The trapped heat can create big issues.

I'll put a thermometer between mine and check the temp.

There are vinyl storm windows, it just isn't the best material for that application, as it is not very strong without boxing and chambering. If you are asking why they don't make storms specifically for vinyl prime windows, it is not the fact that they are vinyl that creates the issue, it is the low e on the glass. I still wouldn't recommend it, but you'd be less likely to have issues if you are putting it over clear glass. In addition, they really aren't necessary as today's windows offer a much tighter seal and thermal performance than old single pane windows.