Depending on what you mean by "needs a lot of signalling bandwidth" I think that is incorrect.

I recall the early SMS functionality being added to cellular phones after the introduction of 2G in the early 1990s and as I recall, one claim was it monetised the massive amount of spare signalling capacity on the network. In the UK I recall that being said in 1994 by Orange (the first UK 'challenger' network vs 1G incumbents CellNet and Vodafone) when I had a Nokia 2010 handset.