I only evaluated Shopify for a project, so I have limited experience. But from what I know you don’t need to use their CMS. They have a very well documented API so you can integrate with them as a backend service that just handles the e-commerce side of things. If you go that route it is on you whether your store is slow or not.
Indeed! I've been looking into trying out a JAMStack-style website using the Shopify API [0]. Some starter templates:
Gatsby-Shopify: https://github.com/AlexanderProd/gatsby-shopify-starter
Gridsome-Shopify: https://gridsome.org/starters/platform/shopify/
I wish Shopify's pricing page was clearer on which plan I need to use the API.
What that means depends on the business and the employees. If you got no developers, then maybe your only option is to use something that is ready and needs no development. If the shop is your main business and you got good developers, then you might want to do one better, even if it takes time and effort.
So I would not necessarily exclude the possibility, that creating your own might be best for you. You can still make use of third party APIs for things like credit card payment and so on. When you roll your own, you get to decide which parts you outsource and which parts you make yourself. This allows you to decide where you want to be flexible and where you limit yourself to what the limits of a third party software are.