Plus SMS uses phone signalling, like 2G does, and 3G data a bit. It needs a lot of signalling bandwidth where data and voice, ironically, do not need as much. SMS will fail long before data or voice on cellular networks fails. It has retry, which is famous for sometimes taking actual days to deliver a message.
Doesn’t apply from 4G onwards, where everything is IP, but still.
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.
SMS or signaling cannot use the bandwidth used for voice, they are entirely separate. On 1G and 2G one SMS needs the same bandwidth as 8 calls to go through. The signaling line can run at insanely low bitrates (and there may be errors).
The main problem was too many phones in one place causing errors on the signaling line. Like a concert. You'd get to a point where maybe one call can go through every 10 seconds. Then one person tries to send an SMS "because he can't get through" ... and the phone helpfully keeps retrying to send the SMS, each retry causing >1 minute of nothing signaling on the network. The network is now dead and while existing calls work fine, you can't even hang up anymore, never mind making or receiving a call.
Doesn’t apply from 4G onwards, where everything is IP, but still.