I have seen weather balloon measurements of air.
Why is this done? Aren't the measurements we take on the ground enough?
The reason is that we need them! And we could probably do with more of them (e.g. bigger launch budgets).
Surface observations will tell us where fronts are, where low and high pressure is, and how surface temperature and moisture are being advected. We can also deduce large scale ascent or descent (vertical motion) from surface divergence and convergence. We might even be able to provide very short term forecasting, though the skill won't be great. To know how the surface will evolve you need to know what is going on above the surface.
If we know what the 500 mb surface looks like, we can combined this information with the surface fields and some quasi-geostrophic theory and do better with short term forecasts. With just one upper air layer we can see how the feedbacks between the mid/upper-troposphere and the surface will behave and better predict the development and motion of low pressure systems.
To provide more accurate forecasts, have a shot at predicting convection, and provide longer term forecasts we need more information about the vertical structure of the atmosphere. The current state of models are such that one of the best things we can do to improve them are to provide better initial conditions (better observations and more of them). Balloon launches are a great way of getting this data. Ground and satellite based observations can provide parts of this, but we still benefit from being able to directly sample the atmosphere and to calibrate the remote sensing algorithms with the radiosondes.
One example of the necessity of balloon launches is in convection. Knowing only surface convergence, temperature and moisture is important, but does not tell the whole story. If the 850 mb temperatures are too warm, it won't matter how good the surface observations look, you won't get convection. How much energy the storm can tap into depends on the temperatures all the way up to the tropopause (and higher if you want to know how high the cloud tops will be). Knowing what type of storm to expect depends on knowing the winds in at least the bottom 6 km of the atmosphere. Having vertical information provided by a radiosonde is the difference in only being able to say "the air is warm and juicy" versus being able to say "expect isolated supercells today with large hail and straight-line wind damage" or "despite the high dew points, the capping inversion and associated CIN will suppress all convection today -- no storms" given the exact same surface observations.
And yes, models can give us the upper air structure to base these kind of statements on, but remember the radiosonde launches are where a lot of the upper-air data comes from that allows the models to work well comes from.
The atmosphere is dynamic both horizontally and vertically. You cannot provide services like weather forecasts without a true measurement of the atmospheric conditions in the troposphere and stratosphere across the globe. Satellite retrievals also rely upon measured vertical profiles for calibration of the final products.
Radiosondes are an essential source of meteorological data, and hundreds are launched all over the world daily. Worldwide there are more than 800 radiosonde launch sites. Most countries share data with the rest of the world through international agreements. Nearly all routine radiosonde launches occur 45 minutes before the official observation time of 0000 UTC and 1200 UTC, so as to provide an instantaneous snapshot of the atmosphere. This is especially important for numerical modeling. In the United States the National Weather Service is tasked with providing timely upper-air observations for use in weather forecasting, severe weather watches and warnings, and atmospheric research. The National Weather Service launches radiosondes from 92 stations in North America and the Pacific Islands twice daily. It also supports the operation of 10 radiosonde sites in the Caribbean.
Forecasts that incorporate the 3-dimensional structure of the atmosphere are more accurate than those that only use the surface structure.