I don't understand the tradeoffs you're listing--is it because you are locked into a particular line of cabinets with limited options? There are lots of shaker-style frameless cabinets. And frameless cabinets with glass doors.

"We love how clean lines but would have to forgo the shaker style we love and glass in the top cabinets."

That is not true - you don't have to forego either of those. Frameless cabinets most certainly can have Shaker door and drawer fronts. Frameless cabinets can most certainly have glass-front cabinet doors - I have them. Is someone telling you those things, or did you just assume those things on your own?

Anyway, the advantages of frameless cabinets are, as you said, the clean lines, and also the additional interior space of frameless. People on this forum will poo-poo the additional interior space, don't listen to them. I swear to you, the additional space is significant. As an example, framed upper cabinets interiors will be about 9-1/2' to 10-1/2" deep. There are many dinner plates that are larger than that - we've had posts on here complaining about not being able to fit dinner plates in framed upper cabinets. The shorter depth also limits the rows of glasses per shelf. Frameless cabinets will utilize the entire interior cabinet space since the frame is not taking up that interior space. In addition, frameless cabinets do not have the dreaded stiles between doors.

FRAMELESS CABINETS WITH SHAKER DOORS;

I have everything you mention that you want - all frameless cabs, some with skinny shaker doors, some with flat panel doors and some with glass (not all mixed together). Maybe it's your cabinet brand that is the issue?

Why would you have to forgo shaker style and glass?

I have glass and frameless shaker cabinets.