the inability to import DXF's, the inability to show the back of a PCB in correct orientation, the inability to use fonts, the inability to angle copper pours [or do arbitrary pad shapes]
IMO, you have an odd list of "requirements." Perhaps they're important to real commercial PCB design, but they sounds more like "here are some features that I've grown used to in my favorite SW, and EAGLE doesn't have them." Fancy board shapes, fancy pad shapes... That's fine, I guess, but it seems very ... personal. Sorta like me complaining that my convex hull ULP written for EAGLE can't be used in Altium - I might eventually decide that I don't like altium, but I hope I'd have a better reason...
All my stuff is commercial.... the PCB shape/size/layout is almost always driven by something else like an existing housing or a product design requirement that precludes the PCB being the shape it would be if it was designed in a vacuum. But I don't think the requirements are unusual at all.
In the case of the ground plane, IIRC it was for a capacitive sensing board and crosshatching the copper pour was either required by the capsense or by the PCB fab, and not being oriented at 45-deg means all your parts sometimes come between horizontals or verticals leaving very little contact to the ground plane. Cap sensing isn't uncommon.
In the case of fonts on the PCB - I think that is a pretty common need these days. Unless one is just doing hobby stuff, there will almost always be a logo somewhere... I see much more of it than I did 20 years ago.
And as for arbitrary PCB shapes, I think if you look at the vast majority of electronics these days, "swoopy" cases is the norm - the old "heathkit" style of products are a thing of the past. When form follows function, it's rare that a PCB can be rectangular.
Arbitrary pad shapes... I use a lot of power LED's, regulators and FET's, and they all (especially LED's) are increasingly using uniquely shaped land patterns. I think LED's are one of the biggest areas of electronics these days, and from reading various forums, a lot of people have this same issue.
These aren't things that I searched to find wrong with Eagle, these are real limitations I've run into over the years that were a pain in the ass to solve. Another is component creation - my hasty and faulty off-the-cuff example above aside, surely component creation isn't a special case? Some datasheets reference pads from a point, some are relatively positioned. Some use centers of pads for reference, some use boundaries of pads. Take an arbitrary pad shape referenced from the edge of another arbitrary shape at angles to one another, and something that would take seconds to draw in AutoCAD can mean a lot of scribbling and measuring to calculate the coordinates required in Eagle.
And speaking of messing with coordinates, panelization is another total kludge in Eagle, and when you start wanting to do v-scoring or add rat bites, or pull traces onto the panel (like in Dave's video where he had programming/testing traces unique to a panel) - that breaks annotation and makes your board un-editable. Surely panelization isn't an esoteric requirement?