I think I agree if you mean by compound that sidewall stiffness and rubber compound to get the V versus H speed rating makes a difference in how you perceive and your satisfaction with a tire. Relatively stiffer sidewalls could be expected as speed rating increases. The tire itself would have to handle more heat to get the higher speed rating - though I'm not sure how that would be perceived by the driver.
So if you want a tire designed for performance you might consider this is implied by speed rating.
But H versus V is only one step. It is bogus to suggest any safety, insurance or warranty impact. And, sometimes same brand, model and size is available as H or V (V costing a few dollars more). If that is the case assume the tire is legitimately rated V and you are going to get the same tire regardless. Look at the reviews for a specific brand and model tire and see how they are marketed - these inputs as much as anything tells you something about the design goals and whether it is a tire that you might like. Every tire trades off comfort, performance, wear at a price point. What one person concludes is a great value the next might feel very disappointed.
