We utilize a never-engaged segment for exclusion in our campaigns every time so it’s good practice if you haven’t decided to suppress them completely (especially for emails).
But for SMS, break your list out into 4-5 segment-based engagement windows: 15, 30, 45, 60, 90+ day depending on your cadence, then start analyzing which groups are most engaged. You can then decide how often you communicate with each audience. IE: if you’re sending a campaign every week, maybe you only send that weekly to the 15 and 30day engaged and send the most important campaign of the month to all of them.
Just some ideas :D