When picking a font in xfce4-terminal (tested with 0.8.9.2-1 as packaged in Debian), the font picker offers a selection of all fonts. On systems with lots of fonts available, it is very hard to pick a font, because all the fonts appear, and the GTK dialog does not give the user an option to narrow it down to fixed-width fonts.

I was just about to open an issue with GTK to pretty please add a way to narrow things down by font properties (as good ol' xfontsel could since the dawn of X) when I checked back with gnome-terminal and noticed that they do limit the options programmatically.

Unless the GTK dialogue grows the ability to do more than scrolling through endless pages and search by font name (where some but not all monospace fonts have a "mono" in their name), I think it would be a good choice to follow gnome-terminal's behavior and limit the dialogue's selection to fixed-width fonts.

Some useful pointers might be https://developer.gnome.org/gtk3/stable/GtkFontChooser.html#gtk-font-chooser-set-filter-func and https://developer.gnome.org/pango/stable/pango-Fonts.html#pango-font-family-is-monospace .