Yamaha already has several lines of keyboards with piano-style keys, ranging in price from under $200 to over $1000. These include, but are not limited to, the NP line, the P line, the YDP line, and the DGX/YPG line.
The least-expensive model seems to be the NP12, with 61 box-shaped keys, which is currently listed on Amazon at $180.
All of these lines have piano-style (box-shaped) keys, but some are just semi-weighted (I think they're "Graded Soft Touch"?), while others are fully-weighted ("Graded Hammer Scale").
Most of these "piano-centered" lines don't have nearly the number of voices, styles, and other features as the PSR-E and PSR-S arrangers. The DGX/YPG line is the closest to being a "piano-style arranger," but is XGlite-compatible rather than XG-compatible, and can access only the A and B style variations.
Of course, there's also the Clavinova line, which is also a piano-style arranger, and fully XG-compatible, but much more expensive than the DGX/YPG line.