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Store design apps are made to help you fix a specific on-site problem that you're having, whether it is tweaking a product detail page, adding a sidebar to a blog post, adding swatches to the site, or changing the layout of your homepage. These tools are mostly about design and layout as opposed to other tools that are focused on conversion rate optimization directly - tools like review and social proof tools, or countdown timers.
Store Design tools are used in lieu of custom coding or paying a designer/developer a hefty fee. These tools are typically a shortcut to a certain solution that you need.
You've got a specific problem like needing 150 variants on one product, or switching the product image when I select the "brown" color, or something like that. That's when a Store Design tool will really come in handy. Most of these tools are cheap, monthly recurring, and solve your problem completely.
In some cases or as you grow you may want to take out a Store Design tool and build it yourself or with the help of a developer. It may cost more up front, but lowers the monthly fees, and typically can be better optimized for your given circumstances.
The head of Ecommerce, your store developer, or you, the solo-founder. Most of these tools are set it and forget with little ongoing maintenance needed.
The one functionality you must be concerned about is page speed load time. Make sure this tool loads asynchronously so as not to slow down load time. I also recommend investing in tools from the more reputable app developers to help reduce the likelihood of this app causing the website to go down, or breaking another app.