https://us.espres.so/products/espresso-pro

This is a 17" 4k, portable display which would bring back the ability to directly write on music with the required accuracy.  The height is 15.6".  The historic height of staff paper is 12" but 15.6" is the smallest with 4k. 

Of course, you'd have to be stupid to pay that much & it would take 2 monitors to fully to the job but it showed considerable improvement in portable monitor offerings.

There's 2560x1600 in a 16" without touch. 

The pride of China is a 15.6" with touch & 4k. 

Then for the same price of 2560x1600 is 4k from another brand.  Lions doubt the truth of some of these chinese deals.

https://www.walmart.com/ip/XGaming-16-120Hz-Portable-Gaming-Monitor-2-5K-2560x1600p-QHD-IPS-Laptop-Monitor-Dual-Type-C-Mini-HDMI-HDR-PC-Mac-Phone-Xbox-PS4-PS5-Smart-Cover/2341421537

Then there's a Walmart deal.  2560x1600 might be the sweet spot. 

Lions couldn't justify upgrading the current music display, given its level of use & how 1366x768 has been just good enough.  1366x768 would definitely be enough for composition.  The higher resolution would only be needed for annotations, more serious playing, or maybe a more expensive instrument.