(Note, the producers Sony is who really made the decision of replacing Dan Harmon as show runner for Community. But for all intents and purposes I'll treat NBC as the final word on decisions regarding the shows they air)
If you like the show Community you'll have heard about the controversy regarding showrunner Dan Harmon. The show got renewed for a final 13 episodes in season 4, but his contract didn't. The outrage is that Community is so intertwined with Harmon's personal vision and touch that the show should not exist without him. It's like if someone released a "Sheryl Crow album" but instead of her being involved they just found someone to replicate her voice. It crosses a line in artistic merit and severly pissed off a rabid internet fanbase, who frankly would prefer the show just got outright cancelled, a fate all of us have seen before for our favorite shows.
I'm not going to dispute the immediate financial reasons for this move. Technically the show may have a better chance at long term viability if they attempt a more traditional style of humor for the next 13 episodes. Frankly the only reason it was renewed was to bring it to syndication length. In the mean time they threw a hail mary in regards to it attracting a new audience with a new showrunner, I assume. That or Dan Harmon's infamous difficulty to work with and propensity to go over schedule and budget is what cost him his job.
However what NBC is missing is this isn't just about the short term profits. What smart businesses understand, in TV/media and elsewhere, is the importance of the brand and building loyalty in the customer. The more well treated the customer is, the more they trust the brand, and the more they come back to their products. Smart companies treat every individual customer with this respect. What NBC doesn't realize is that the minor financial benefit from releasing Harmon is likely outweighed by antagonizing a certain number of viewers. Community was not a great ratings performer, but we're still dealing with a number in the millions for viewers. NBC could be directly antagonizing somewhere between 2 and 3 million TV viewers who are choosing between it and competition. There may also be a multiplier effect where many of these viewers bring up their distaste for NBC with conversation with friends, on facebook, twitter and on blogs, and likewise anti NBC sentiment spreads. Now the number of viewers who hear the words "Fuck NBC" grows past the original fanbase. Perhaps 10 million people or so encounter anti NBC sentiment because of this. Are they going to consciencely vow to stop viewing the network? No, but subconsciencely the brand is damaged by this negative publicity. It's the opposite of why television advertising is effective. Advertising may not make viewers jump out of their chair to buy the product, but it implants a positive image or idea in their mind of the product and when it does come time for them to buy it, that impression of it makes a significant difference. NBC cancelling Community achieves the exact opposite of effective advertising, they might not vow to stop watching NBC, but the bad taste in leaves in people's mouths may very well have a subconscience impact on whether they choose to watch NBC shows over an alternative later. Bad publicity is not always good publicity. Finally, the idea of losing the respect of viewers may not only come through the ones upset with this decision, but the ones who aren't aware of it, watching a potentially downgraded and mediocre version of Community next season, and then leave their period watching the show with a much worse taste in their mouth of the product than they would've if Harmon put out 13 more great episodes. There is a value into putting out the best product possible - again, it's because it builds respect for the brand.
What it reminds me of is what I've become convinced is NBC's biggest mistake of the last decade. When they made the decision to replace Conan on the Tonight Show with Leno in early 2010 - a big mistake on their own, they compounded it with a bigger one. Instead of doing everything they could to quiet the flames and controversy and sweep it under the rug, NBC poured gasoline on the flames - They gave Conan 2 weeks to absolutely annihiliate their reputation and brand on TV, of which many people caught up on the clips via the internet. The Conan sympathy story became a national one and everyone for those 2 weeks was talking about it. NBC bought into it and let Conan kill them on TV because it got them short term ratings. What I believe they underestimated is the damage to a brand and reputation something like this can do. The amount of people who had "NBC sucks and is unprofessional and go Conan" type of phrases pounded into their head was immense. It was the ultimate anti-advertising campaign, like a politician funding the negative ads destroying his own reputation for a quick buck. People may have not jumped out of their chairs to say they're not watching NBC, but I truly believe that subconsciencly all that negative publicity had to play a part in how much of the brand people respected, trusted and wanted to consume the product of. Somewhere in the last 10 years NBC went from a respected powerhouse to a joke and I believe that was one of, if not the biggest turning points. They sold their reputation out for the short term returns of Leno back in the Late Night spot and then the immediate ratings Conan's farewell shows gave them. A more stable network may have realized the best decision long term may have been to put away that mess as quietly as possible.
I don't think the negative press from Community's renew botching is as large as the Conan fiasco. But I believe it will still do more damage than good for NBC. The biggest reason they've fallen off so far in the last decade is simply not having as good a product, but antagonizing 2-3 million people of the loyal fanbase they have left, is a huge mistake. The more NBC has the perspective where mistreating its customers who like one of their products + ignoring the idea that aiming for the best quality is what will sell and save them, like most businesses who are disconnected, the more they will fail and collapse financially.