The former could be addressed by expanding the escape sequences sent by the PC-style function keys, while the latter was a VT100/VT220 design issue. I decided to redesign function-key support to separate the two styles of function keys better, but leaving the choice still controlled by the sunKeyboard resource. Partway through that, I was asked to do similar cleanup and redesign of the backspace and delete key handling, ., the ptyInitialErase resource. Because it is a redesign, I chose to not make the keyboard differences between the old and new xterms completely compatible. If you were to run both on the same system, one or the other would have some problems with the editing keypad or the backspace/delete keys which would be addressed by the popup-menu selections.
The entire system runs smoother if TERM is set properly. Overriding it to incorrect settings can produce strange problems which don't exist when using a different terminal emulator. The existence of poorly written terminal emulators using bogus TERM values results in application developers "working around" issues with their Terminal applications which, in turn, causes Terminal applications to not behave as you would expect. Now we have terminal applications sending color escape sequences when the terminal is monochrome, and we have some terminal application forcing xterm-style 256-color codes to terminals regardless of whether the terminal supports it. It makes me sad, as it is bad design breeding more bad design.