Think if its been sitting there for 200 years, somebody would fix it up and fly the heck outta thur like thur right thur? lol...
Because there arent exactly a lot of trained Aircraft Mechanics lying around. Aeroplanes are complicated machines, even simple ones.
I've actually written an article on what Aerospace technology could exist in the fallout universe - I've kinda misplaced it, but here is the basics. Note this is speculation and supposition on my part.
1) Hot air Baloons - Probably exist in moderate and higher technology groups. Textiles and some gas burning technology required. Probably owned by richer eccentrics for pleasure, and used by organised governments (NCR, Vault city, etc) for scouting, cartorgraphy and aerospace research.
2) Lighter than air baloons and Zepplins - Helium aircraft (like blimps are today) are probably non existant due to the difficulty in getting helium. This leaves Hydrogen, like the Hindenburg used, which is plentyful and relatively easy to produce (Any water source, even if undrinkable + Electric Current = Oxygen and Helium). Known to exist in the BOS (if Tactics is taken as Canon). Within technological grasp of the NCR, Shi, and Vault City, although the NCR is more likely than the others to build them it due to better resources. Can be used for transport, as well as scouting purposes. Probably out of reach of the regular citizen, although richer caravan masters may have an interest in this technology to get above the raiders.
3) Fixed Wing Gliders - Essentially an aeroplane without an engine. They can take off by various sources, such as another fixed wing aircraft towing it, a winch (essentually an engine with a long cable), an Auto-Tow, or a bungie launch from a hill. The Current standing endurance gliding record is over 56 hours, and was set in 1952 (new records stopped being existed at this point for safety reasons), showing that long term flights without an engine are possible given pre-divergence technology. This would require some degree of civil control (as an airfield of some type would be required, and would need to be maintained) and technological development (to build the aircraft structure and launch method). Gliders can be used for recognissance and transport (tanks and troops were transported by glider in WW2). Shi, NCR, Vault City, and the Brotherhood are all potential users of Gliding technology.
4) Fixed wing power - Aeroplanes. Some level of civil control is required to operate and maintain an airfield, and a good understanding of technology is required to build and maintain. AvGas (Fuel) is likely to be extremely rare, so any Fixed wing flying is probably limited unless alternative fuel sources are available. NCR and Vault City, with their access to pre war vaults (and the Vault library contained within) could possbily build a fixed wing aircraft. Brotherhood is a possibility, depending on the source of their library. Shi are less likely without these sources, but due to their organised scientific culture have the capability to rediscover the secrets on their own (if they cant find a source in an old San Fran Library somewhere). This is probably the minimum level of flight technology the enclave would show, however due to their lack of territorial control would have some trouble showing this power.
5) Helicopter / Vertibird. A Heliport is probably easier to control, operate and maintain than a full runway airfield, but helicopters would require a good technological understanding and capability. Enclave show this capability. NCR and Vault City with their access to Vault Library computers might be able to build some elementry helicopters. Shi and Brotherhood may have plans and capability to build vertibirds, depending on how you finished FO2. However, fuel is likely to be a problem.