Is there any reason nowadays to use a neon indicator lamp instead of an LED?

Neon bulbs use microamps of current when fed through a dropping resistor directly from the AC line. LEDs need 10× to 100× the current and can't be fed AC directly.

I think you'll find neons have more resistance to ESD, transient overvoltage, and high temperatures.

You can do many interesting things with neon lamp circuits, all of which are curiosities in 2019 (well maybe they're useful if you need EMP resistance, but I suspect we'll have bigger problems if that's a factor). Neons wear out, for one thing. From the above document:

When I were a lad, I designed a monitor system for Linotype machines (yes, that long ago) using a neon bulb oscillator triggering a then-newfangled C106 SCR (in that horrible package with the 0.05" nominal wide leads), to operate a stepper relay with precious metal contacts multiplexing thermocouples.

I don't see any real reason other than to save a few pennies to use neons as indicator lamps. An NE2H runs at around 2mA, which is sufficient to give more brightness from a decent LED (not all packaged indicators use decent LEDs, however). The neons will wear out if they're powered constantly (rated life is 12,000-25,000 hours which is less than 3 years 24/7).