Having spent two and a half years of my life getting intimate with GSM-based (ie, not CDMA, though a lot of the protocol stack is the same) SMS messages (I worked for a company that did security, anti spam, anti fraud and other VAS systems (parental control, blacklist, SMS backup etc) for mobile operators)[1], I know a little bit about it. Admitedly I could tell you a lot more about the protocols used by SMS than its history

GSM networks consist of two signalling links: voice and control. The contol is used to, for example, set up or terminate voice calls. This meant that, in practice, the control signalling links were generally idle and so they piggy-backed SMS on it. I don't know anything about the 128 bytes, but the 160 characters comes from the 140 byte payload, when using the 7bit GSM default packed alphabet. I don't know the numbers offhand (been a year since I've worked there now), but quite possibly this is, indeed, the maximum packet size available, though there certainly is a large range of differently sized packets. In fact, a lot of things are piggy backed on the SMS payload. For example, when using concatenated messages (or binary data - there was a range of predefined things that are biggy-backed on SMS as "user data"), the header telling the phone which message it is is placed at the start of the message payload (reducing the maximum characters per text by (I don't remember offhand anymore) ~6 octets. Of course, 160 characters only applies to the 7bit GSM default alphabet. SMS messages also support 8bit and 16bit payloads.

Mobile operators absolutely love SMS as it is probably the most expensive form of communication they offer.

Somebody else below mentioned ubiquitous internet as an SMS replacement. While I think its true for a lot of people in well built-up parts of the world (and who have a smart phone, a lot of people still don't), its certainly not global. Hell, even here in Ireland theres areas where cell phone reception is pretty bad, so while you might manage to send or receive text messages, if you want to go online you're out of luck. Other, poorer, parts of the world are even worse off. Actually, I remember one company at the 2009 GSMA Mobile World Congress in Barcelona was demonstrating a solar panel powered mobile cell tower, for use in places like Africa, which was designed to provide better coverage of mainly SMS to large open spaces.

[1] http://dublindan.posterous.com/things-ive-worked-on-4 We did a lot using transparent Home Routing http://en.wikipedia.org/wiki/SMS_home_routing The wikipedia article says that transparent home oruting is limited. I disagree. At least in the lab, we implemented everything from the technical realization (and then some) on a transparent home routing system. I believe when I left the company, others were working on a non-transparent version too (because it is easier/cheaper to get and install hardware for non-transparent operation than for transparent). But then, we did a lot of non-standard things, we just did them in ways that don't interfere with the rest of the network.

EDIT: comment didn't end up as interesting as it sounded in my head. Hopefully somebody found it useful nontheless.