It depends what you mean by elderly.
If you're using it to describe somebody's frailty or lessening health/abilities, then that could happen to anybody at any time and isn't just the preserve of the advanced in years, so it's unconnected to any particular age landmark.
If you're using it to describe how many years they've been on Earth, it's irrelevant to say 'my Grandma is 105, dating a 21yo Chippendale and still goes hang-gliding in the Himalayas so she's definitely not elderly yet'.
I think it was probably originated to sound kinder than just using the less-arbitrary word 'old', but if anything, the reverse is how it's come to be understood, with people attaching personal judgments as to what it means and thus rendering it pretty meaningless.
It seems to me to be another shortcut to stereotyping people and forcing them into a descriptive box rather than treating them as individuals - similar to how some narrow-minded people believe that a girl who hates dolls, dresses and unicorns and loves rugby, jeans and trucks isn't simply an individual girl with her own personal preferences but must indeed actually be a boy, in order to shove her into a convenient stereotype.