I'm going to emphasize the benefit of retaining "complete control of your website" with WooCommerce.
On 12/14/2020 Google experienced a global outage, which was subsequently linked to an "accidental" reduction of capacity in their central user ID management system. In simple terms, someone at Google decreased the capacity in the resources settings and suddenly accounts with OAuth-based authentication could no longer be verified, accessed or even communicated with (if you sent an email to a Gmail account during this time, you may have gotten an error, stating that this account does not exist).
Not surprisingly, this global outage affected Google Cloud. And guess who partners with Google Cloud? Shopify! During this outage, if your website was hosted through Shopify, you were down. Once Google diagnosed and restored the capacity, you then had to reboot your system and (in some cases) re-calibrate your server settings, before your website would work properly. You then had to triage and develop a response to your clients or customers who were affected by the outage.
Therefore, as much as I recognize Shopify's superiority in ecommerce systems and capabilities, who is really in control of Shopify websites? It's certainly not the website owner. To me, Shopify is analogous to Apple. Despite having cutting-edge, rock solid systems, its users are always at the mercy of its equivalent of iTunes, iCloud and so forth.