Your account with your carrier involves connectivity with your carrier's cellular network. That connection allows low-bandwidth services like phone calls and SMS texting to occur, no matter if you have WiFi or mobile data enabled or disabled. Both phone calling (mono-only audio signals that are highly compressed) and basic text messages (minuscule text files) do not require a lot of bandwidth so they both only require that base cellular connection to work.
Deactivate your SIM card if you want to stop text messaging (...and note this will also stop your phone from receiving phone calls).
When you do need to do anything that requires more bandwidth -- emailing, video calling, text messaging involving attachments (MMS), etc. -- than yeah, you do need to enable WiFi or mobile data.
Basically, you have always have that basic cellular connectivity (that's your account with your carrier), it's just that mobile data works within that connection. Theoretically you can use your smartphone with no SIM, no cellular service account and just rely upon on independent WiFi Calling services (i.e. Google Voice) and only WiFi connectivity but that's a stretch in a lot of situations since WiFi access isn't always available wherever you go. (...and it's really important to account for the all the security and privacy vulnerabilities when using public WiFi networks.)