If you look at page 202 of the PHB, you will see a description of range in the spellcasting context. I will draw your attention to the final paragraph on that page, "Spells that create cones or lines of effect that originate from you also have a range of self, indicating at the origin point of the spell's effect must be you (see "Areas of Effect" later in this chapter)."
This informs the discussion in two ways. First, it says flat out that the range of cones and lines originating from the caster is self, not self (but really) or self (plus). Second, it distinguishes between "range" and "area of effect" as game terms. Range, definitionally, is distance to the point of origin, while area of effect is the form the spell takes from the point of origin. In cone and line (and other) spells originating from the caster, the caster is tautologically the point of origin. The description in parentheses after "self" is the area of effect. Just as you cannot increase the radius of a fireball with distant spell, you cannot increase the length and radius of a cone of cold.
The one screwball that I know of offhand is sword burst, which has a range of five feet and no area of effect; it simply effects everything in range. That does work with distant spell.
Ah, makes sense.
Besides Sword Burst, Beacon of Hope apparently works like that too.
Telekinesis deserves special mention, because it allows you to move people/objects to the extent of its range, so if you're lifting and dropping things double the range is double the height and therefore double the falling damage.
Overall, though, that's a very short list. And the other uses --just doubling range, and extending touch spells to 30'-- seem very lackluster for a metamagic choice, unless you happen to be a "reach weapon with booming blade" build. I think Distant may take the cake as the worst metamagic.