To be completely honest, this is an overreaction. Yes, peanut dust can cause problems, but the problem comes much more from contact with contaminated surfaces (e.g. armrests, tray tables, etc.) from passengers on the previous flight than from dust transported through the air. Cleaning your seat environment with an alcohol wipe or similar before taking your seat is going to make a lot more difference than banning someone 15 rows away from eating peanuts in flight.
Contrary to popular belief, airliner air is actually quite clean - significantly more clean than in most buildings. If you don't have a reaction from someone on the other side of your restaurant eating a peanut, then you're not going to have one from someone sitting on the other end of your plane eating peanuts, either. Airliners actually use quite good air filters and around half of the air is not recirculated at all, but rather dumped out the outflow valve and replaced by outside air (from engine bleed or a scoop.) So, the odds of any significant amount of peanut dust from someone in row 30 reaching an allergic person in row 10 are extremely remote. The airflow is spanwise (from aisle to window,) so only someone within a few rows of you is likely to breathe in any peanut dust you may generate.
According to a study published by the National Institutes of Health,
The vast majority of U.S. airliners use high-efficiency particulate air (HEPA) recirculation filters for cabin air, and these filters are highly effective at collection of solid and liquid particulates.
And according Patrick Smith's Ask the Pilot, due to the fresh outside air mixed in, "there's a total changeover of air every two or three minutes." This is significantly faster than you'll get replacement air in a commercial building, let alone your home.
The only reason that actually makes any real sense for banning everyone on the flight from eating peanuts rather than only the people in nearby rows is that it does not reveal who actually has the allergy, so it's not as embarrassing for them and they don't risk glares or potential harassment from other passengers upset about their lack of peanuts.
As far as whether this is common practice, there are indeed several airlines that do this.
For example, Delta's policy:
If you have a customer that has a peanut allergy, please contact Delta Sales Support or Delta Reservations in advance to have the peanut allergy information noted in the customer’s PNR.
When Delta is notified that a customer has a peanut allergy, we’ll refrain from serving peanuts and peanut products onboard the flight. We'll also advise cabin service to board additional non-peanut snacks, which will allow flight attendants to serve these snack items to everyone onboard.
On the day of travel, customers should notify the airport gate agent of the peanut allergy, if they would like to request to pre-board and cleanse the immediate seating area.
Unfortunately, even with all the above precautions, we still can't guarantee that the flight will be completely peanut-free.
For those unfamiliar with the industry jargon, "PNR" is "Passenger Name Record" and is just the airline industry way of referring to your reservation.
Southwest stopped serving peanuts entirely last year. To honor the occasion, they set up a tongue-in-cheek display case of peanut packages at MCO.
American Airlines does not serve peanuts and allows allergic passengers to board early to wipe down their seat environment.
United Airlines does not serve pre-packaged peanuts on their flights.