That's not a rule. It's a narrative device.
If you tell a story that spans a long period of time, you might invoke an excuse why the people in your story did not have an industrial revolution. And for that it is basically not needed at all, because you only show a certain point of time in the story. In other words, the setting might feature an industrial revolution in the future. Our own world does feature very long statis periods where nothing much happened. This is nothing that needs explaining.
Also neither LotR nor HP did bring that excuse.
The magic users in the world of Harry Potter exist parallel to regular human history and tech advancement. The tech advencements are happening. And some of those human inventions are used by magic users. Like bureaucracy. Writing. Even cars and houses. Or iconically: trains. And the excuse why they do not use more, is cultural contempt for human things.
And the people in LotR just did not use everyday magic to solve their mundane problems. Mostly because they just have no magic. Magic is not a trade to be learned there. Gandalf is not a scholar, he is basically an arch angle. The stasis there is more a cultural thing and not a technology question. No great changes in kingdom borders happened over thousands of years. Then again they do have those elves that live those thousands of years. "I was there 3000 years ago" and all that . Even human races that live a really long time. Aragorn got over 200 and the dwarves also usually have live spans of centuries. But that is also just serving as excuses for the stasis.
I wonder why no one else does it
This is done in all shapes and forms. A popular one is shifiting the industrial revolution a bit and having tech work like magic. All of Steampunk works like that. And if you want to go further, you can even have Clockwork tech.
For games, they usually just do not build a complete world. They focus on some aspects.
But even in a magical fantasy setting, you might see an "engineer", that builds pseudo magical effects with apparatus and chemicals.
For true world builing one should consider the effects on a society. How limited is magic. And what can people do with it. How costly is it. If you have to sacrifice a goat every time you want to heat up a kettle of water with your fire magic, that's not gonna happen. And if every human can spark a fire by snipping a finger, that society probably never invented flint and steel, let alone a lighter.
And I am not sure what you mean by techno magic. There is science fiction settings with magic, Even psionic abilities can be considered magic and often appear in sf stories. And one will find examples how those will interact. I am currently thinking about super hero genre. What those heros do is basically magic by another name. Wolverine has future tech implanted into his bones, otherwise he would just be a regular dude that's hard to kill and he has some retractable bone knives. Or that telepath that went into this huge contraption to boost his telepathic powers. That's what I would call a combination of magic ability and tech.
But I guess you are more interested in the world building aspects of societies. How tech and magic interact, when one exists and the other gets introduced. Or how they evolved together. If you introduce tech to a magic world, it is suddenly the mundane people wielding powers that previously only magic users could harness. Like throwing fire balls.
Also, Shadowrun set in an alternate future in which cybernetics, magic and fantasy creatures co-exist