How can I set text to appear at exact left of frame in InDesign? When left aligned, text still appears slightly inset within the text frame.
Can it be made to align to the exact left edge?
No, you cannot. There is a very simple reason for this too. All characters in a font have a little bit of whitespace to its left and right side. Without this, the characters would touch each other (in the current font design systems, anyway).
In addition, it's debatable what 'the left edge' is, for any given character and/or font. For instance, do you count the serifs of a serifed font or not? For a sans serif font, it's usual for round letters ('O', 'U') to stick out at the top and bottom; would that need to happen to the left as well? Also, if you look carefully to an Arial uppercase 'A', you will see it already sticks out to its left; so would it need sticking out yet even more?
But depending on your final goal, you can use different tricks to work around this in InDesign.
For a text frame: Move your text frame's left edge to the left, to the position where you want the left edges of text placed.
For a single line: Insert a Hair Space before the first character on the line, then use Kerning to decrease the space between the hair space and the first character until it's where you want it to be.