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H. G. Muller wrote on Wed, Apr 19, 2023 09:59 AM UTC:

Perpetual checking is also a concern. A flying Queen would be much to good at that. In Tenjiku Shogi that is not a problem, because repetitions (other than check evasions) are forbidden. (But even then it can take a long time before a flying Queen runs out of new checks.)

Something would have to be done against this, or players would just preserve their Eagle until the board population thins enough to draw by a perpetual, when they are in danger of losing. Where a Rook on a near-empty board cannot check a King forever (so that the Raven is not really a problem), and the color-bound Bat is no problem at all, we know that even a single piece to shelter behind is woefully inadequate defense against checking by a Queen.

A similar problem could occur through perpetual chasing. But only the Terror is worth more than an Eagle; other pieces can simply be protected when the Eagle attacks them. This is a second reason to extend the anti-trading rule of the Terror to capture by an Eagle: if capturing a protected Terror is forbidden for Eagle as well as Terror, the latter can be protected too to put an end to any chase.

The Eagle should definitely be able to check a King, though; that was the entire point of including it. To not interfere with normal chess-like play too much, the repetition rule could state that it is forbidden to repeat a position through a move with an Eagle that delivers check.