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Allowing for taking the king - feature suggestion

Why dont you play antichess if you want to capture the king?
I still think it would be an interesting and fun variant. With deference to your teaching experience, it would be a simple variant of chess to play with people who are just starting. Just as with many things different people learn different ways. Complex subjects can be broken down into steps. 'Capture the King' can be explained very easily (explain the moves of each piece, explain how to capture, and go). Later it it may be easier to introduce the idea of checkmate and the prohibition not to move into check, progressing to the venerable game we all know and love. You may not approve but some may find it helpful and or fun (like the original poster).
I am not asking to redefine Chess, I am just suggesting:

(i) a new chess variant, that can be fun and interesting on its own right, and

(ii) that it should be easier for children and other beginner to pick up this variant, hopefully with the help of lichess puzzles, before moving on to Chess proper.

There is nothing wrong with considering other variants, and lichess already offers some of them.

Also, in teaching a concept,or a game, there is nothing wrong in starting with incomplete, more manageable, versions of it, and then building up to the complete picture. (This general approach was even used by Lazlo Polgar teach his daughters, if I recall correctly.)
Tell your daughter, "we are only teaching the king a lesson, so he could be a better person next time. We don't need to kill him". She will understand.
This is an interesting thought. I don't remember being hung up on this as a kid, but I learned over the board. then again, I remember my friends and I enacting dramatic death sequences for the king at checkmate, so....

Have you considered showing her on a real chessboard? Seems like a really niche early chess pedagogy thing that would have a small amount of value to a small number of users.
There are also some in person game variants (usually street/park chess) that allow king captures, but I dunno if it fits for online play. If you look up coffee chess on YouTube, I think they have a king capture rule. So if you don't notice your king is in check, your opponent can take it and the game is over! Even if it wasn't mate. Brutal!
Seems like some people get hung up on this as if the rules of chess should be changed, or it doesn't fit their idea of teaching chess. This is a <variant> of chess which is played out in the wild. To me it looks to me like an archaic form of chess, it would an interesting variant. As for puzzles: not clear how to do this. Puzzles are scored. How can you compare players who use 'capture the king' option vs. those who don't?
Thinking about 'captures' as basically killing a piece, then only going as far as checkmate on the king can seem fine based on some history, where many times rulers who lost a war were not killed. Think of one like Napoleon for example, who was not killed when he lost his war, he just had to abdicate his power and was allowed to live in exile.

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