So I don't think there's any reason why you can't use GTM to implement, except that you are on your own if things break.
Did you end up implementing through GTM? If so, have you been successful? I need to move off of the Shopify Facebook integration, but want to be very careful
I think (only my own belief), that there might be a conflict between Facebook Pixel IDs (one from Shopify and the other from JS or API).
These kind of errors are not logged in Google Chrome, for example (duplicate cookie or local.browser.cache).
Nope, removing Facebook pixels is not at all breaking down, but you should make sure all tags and reference works well with this tracking pixel - to do a clean slate.
(And maybe clean a bit template files)
For reference, now GTM is used as main tracking cookie if you use the Google integration inside Shopify.