The question is nearly always asked because something stopped working. A liner style someone wore for thirty years started looking harsh, or started transferring onto the fold above the lid, or simply disappeared when they opened their eyes. None of those is a reason to stop wearing liner; all of them are reasons to change where it goes.
Why liner is worth keeping. The lash line softens with age — lashes thin and lose pigment, and the skin at the base of them loses definition. That boundary is what makes an eye read as an eye at conversational distance. Restoring it is the single highest-return thing you can do on a mature eye, and liner is the tool for it. Dropping liner to look more natural usually makes the eye look less defined rather than more natural.
Why the old style stops working, reason one: the lid folds. A line drawn along the top of the lid, above the lashes, is covered when the eye opens if the lid has hooded. So the line you drew carefully is invisible from the front and prints onto the fold above it — which is why so many people find liner has transferred upward by mid-morning. The fix is to put the pigment into the base of the lashes rather than on the lid skin above them.
Reason two: hard contrast. A sharp black line on a pale, sparse lash line reads as a drawn-on band rather than as lashes, for the same reason black mascara does — there is not enough lash to carry the color. A softer, slightly diffuse line in a brown, charcoal or taupe gives the definition without the edge.
Reason three: a wing needs a flat surface and a steady hand, and over 60 you may have neither. A wing drawn on skin with laxity follows the slack rather than the line you intended, and it is the most unforgiving makeup technique there is. Nothing is lost by stopping at the outer corner. The hooded eyes liner page covers product choice, and the hooded eyes technique guide covers the placement in detail.