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Signal Alternative with SMS Support
(sh.itjust.works)
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The SMS reliance existed before the name changed to Signal and it was a online messanger ever since so no clue what you mean with that.
Going back to my original comment, I was disagreeing with your recommendation of using the default sms application on your phone, as it is not E2EE. I would want an app that does E2EE with as many contacts as I can (meaning, all contacts that have the same E2EE client on the other side), and only default to regular SMS otherwise.
My recommendation isn't to ditch Signal for contacts that have it to, it's simply to avoid adding another app with access to your SMS if you are worried about security, there is nothing that app will do better than your default SMS app.