Though barometric altimeters must be vulnerable to sudden weather changes, such as a thunderstorm. Or to people cheating by connecting them to vacuum cleaners!
I've had some "interesting" elevation changes from Barometric measurements.
Every 24hrs MTB "race" I've done has a very clear drift in elevations which due to the lapped nature is quite obvious; I guess this is also obvious on long Time Trials too.
The other I've had is as you say when the weather changes suddenly, I once got caught out in a period of heavy rain on the flat bit of Fife, the elevation change was quite pronounced.
This has also reminded me of 3d world modelling from the NASA DEM data, 90m resolution which had some interesting effects, particularly when generating the Firths of Forth and Tay.
One of the easiest measure of seeing how good the source height data is when using maps is to run a line from one end of the Tay Road bridge to the other; it's a gentle slope running from 10m above Sea Level at the Dundee end, to 38m at the Fife end;
Ridewith GPS gives next to no ramp when using Google mapping on screen, and with OSM on screen gives a long ramp at 0.2% before a sudden spike a the fife landfall.
This is an issue for me as I tend to switch between the different map options when planning a route, so it's not unknown for me to have a sudden change in elevation profile on my planned routes as i've switched map to check where the next click should go. (You can also see this when doing routing as the different map options will result in a different routing algorithm being used)
Meanwhile both my Wahoo and Lezyne records from yesterday show a slope roughly as expected with the odd blip though over the whole ride they disagree by 320m of climb and 2km distance!
The Strava planner appears to use the same heightmap for all maps behind the scenes, but I find their interface rubbish for route planning compared to RWGPS.
Edit:
Missed 2 things
Previously the Tay Bridge data used to show a flat line to the 25ish M mark on some systems and then the land based rise; technically the RWGPS+OSM data is correct as it's showing land form, not route form (see also Taking the Lift to the bridge deck)
Also IIRC Strava use the data from the rides uploaded, so the elevation profile shown is probably taken from however many thousand Barometric data recordings have taken place over the bridge, which is likely why their values are very close to the data released by the Bridge board (it's very nearly spot on)