Most carriers support SMS over Wi-Fi as a part of their Wi-Fi calling implementation. The IMS gateway is available for voice and SMS services.Ability to send messages over cellular or Wi-Fi (SMS is cellular only). There is no cost to send an RCS message over Wi-Fi.
I've read mixed reports of MMS over Wi-Fi not working with some carriers, but this is more likely a misconfiguration of their IMS infrastructure or carrier profile.