This piece is commonly known as an Amazon. It features, for instance, in Superchess, as one of the 'replacements'. Whether the piece is too strong will depend on the context. I have tested its strength, and its value came out as exactly equal to that of a separate Queen and Knight. (No additional synergy.) If you use it to replace Queens in the FIDE setup it becomes very problematic to find trading partners for it, however.
Note that this super-piece is still not as strong as the Chu-Shogi Lion, despite the fact that on an empty board it can reach more squares. The Lion is lacking the distant slider moves that go more than 2 steps, so it can only reach the squares in the 5x5 area around it, that the Amazon can also reach. The difference is that a Lion can jump to all these squares directly, and can actually make two King steps per turn, capturing twice, if it wants. It is worth about 15 Pawns.
The latest WinBoard release supports a variant Mighty-Lion Chess, which replaces the Queen-side Knights by Lions. This leaves the Queens in the game to oppose them, so that at least L vs Q+R trades are available to keep the game interesting. (L vs L trades are forbidden in this variant, like they are in Chu Shogi.)
Anyone ever play with a Queen on horseback? I.E. she can jump like a knight also. Does Qa5 break the game? Or hitting the Bishop Pawns for epic forks? I've already convinced myself it'd be too powerful to be much fun.