99% of the time, SMS messages arrive within 30 seconds of the sender hitting "Send". When you are going to be delayed by 5+ minutes, 30 seconds rounds down to "instant".
As for the inconvenient, I personally HATE getting a call when I am either in a very quiet business lobby, or very loud social event for someone to deliver an essentially 1-sided trivial message ("I am running 15 minutes late"). SMS's are PERFECT for this. They are, IMO, cheap quick and convenient.
Perhaps it is all in the eye of the beholder.
The "killer app" for this situation would be (IMO) to use a GPS-enabled phone with some rudimentary mapping capabilities that would auto-text SMS ETA messages once you are >5 minutes away from the meeting start time and your travel time is also >7 minutes (ie: when it predicts that you're going to be late by more than a couple of minutes). You would have an "app" on your phone that sent SMS messages to your co-attendees (they would NOT have to install, download or use any sort of application just to get this trivial text info). This would increase the viability and adoption rate, as suddenly your friends do not all need smartphones to get some benefit from the app.
In every group there are always outliers, and I see this in some cases with techies who for some reason or another simply REFUSE to acknowledge that their cellphone is anything more than a $20/mo voice communicator. You can't really solve for those situations.
Amongst all the people I've known/worked with, SMS-enabled cell phones and monthly service packages are the norm. Building an app or service on top of the premise that people can easily and cheaply send and receive SMS messages is not, to me, all that grand of an assumption.
My solution above also somewhat applies to your situation, as you would be the potential SMS recipient from someone with an app-enabled phone. Also assuming that the SMS messages is of the "I'm running late" variety, which would be most common for business meetings and social gatherings, the 20c surcharge would not seem to be something that adds up to a ridiculous monthly accrual. As a proportion of the cost (as in cost of a normal social gathering where timeliness is of some value), or value (as in the potential value of a business meeting), I think 20c is less than a rounding error.
As for business meetings, SMS messages almost seem incredibly informal and curt, especially when money is on the line ("We're settling a business deal and you don't even have the courtesy to actually talk to me?").
I'm most certainly not saying that no one should be texting, just that to some people, a phone is a phone, and would prefer to hear someone and chat with them, rather than having short, expensive, impersonal messages flying about. Granted, 20c by itself isn't that much, but when us poor Americans get slapped with charges on both outgoung and incoming messages, it can add up pretty quickly.
If you don't use text messages, fine. But they definitely have their legitimate uses.
I do take issue with the slow and inconvenient part. It's real time and much less distracting than a phone call. If you stick with it for a few days you can type messages at a surprising rate and it really is faster than a phone call. You don't stop what someone's doing and take over when you send someone a text message. SMS has the convenience of email and the immediacy of a phone call.