I ended the article saying "As is, the script has two issues. One is technical, one is not."
Here are those two issues.
The purely technical issue is that if the computer (but not the modem!) is powered off, and then powered on again, the "support person" will not be informed that the computer is up and online again, because the script will not see a change in the IP address. This can be overcome, if it is a problem, in many ways. A simple one is adding a couple of lines to the shell script that cancel the my_ip_address file if the uptime is less than 10 minutes.
The non technical issue is privacy. This "support trick", or any other alternative suggested in the comments, lets the "support person" know whenever the "users" are surfing the Net from that computer. It makes scenarios like "I didn't hear your call because I was sleeping" "No, you weren't, I know you had just turned on your computer" possible.
In my case, this is not an issue because I only do this as unpaid assistance for relatives to whom I HAVE explained all the implications and only AFTER they have explicitly accepted. If they don't like the idea, then the deal is "next time I come to your place, even if it's ten days from now, I'll help you to "fix" your computer". YMMV
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