There are no advantages. Analog meters are inherently inaccurate, hard to read and bulky.
Yes, an analog display can be useful. But somehow everyone in this thread seems to forget that most decent multimeters have an analog bargraph, for exactly that reason. Only, the bargraph is better than an analog meter: it has no lag, no overshoot and decent meters like the Fluke 87V have a bargraph zoom mode that gives you a center-null bargraph with 10 times the sensitivity, which can be used with the rel mode even in the millivolt range, making peaking and nulling much faster and more accurate than with an analog meter. The Fluke 87 original series and 87III even have a high resolution bargraph that is at full scale at 1/4th of the range.
All the bargraphs I've seen on DMMs
do have lag,are too small for easy reading,& are basically just an "after thought",but I'll take your word for it.
It is more than nostalgic clinging to the past-----many people find the analog meter format easier to use.
There is no extraneous information,like a bargraph has----you concentrate on the "needle".
A fast,large display digital "rendition" of an analog meter can be produced,which offers the best of both worlds.
Ham Radio Transceivers tried going the bargraph route,but nowadays all have their "S"meter as a "rendered" analog scale.
Automotive speedometers tried using real digital readouts ,but they were horrible,as it was difficult to see your speed at a glance.
The next thing was digitally driven analog displays,& a very few bar graphs.
Interestingly, mechanical bargraph displays were used for a while in the 1950s & fell out of favour,so maybe bargraphs looked a bit "retro",but not in a good way.
Today,they are a mix of a few bargraphs & many rendered "analog" displays,with most people preferring the latter.