First reason for the Hornets to not embrace the tank: Tanking can have long-lasting negative consequences
The impact that extended losing on a year-over-year basis can be massive. Purposefully trying to lose can result in a black cloud being cast over the organization, making it increasingly more difficult to shed the label of being an afterthought. This can lead to any potential free agent signings down the line opting to go elsewhere, and the players they do sign being massive overpays for their skill level.
The issues with tanking can extend to the players on the court, which creates an even larger problem. If the players on the court do not believe they have a chance at winning, it can create a toxic environment. This can result in a mental block that goes beyond the current roster and can spread to future versions of this team.
Losing on purpose can lead to a team being stuck in a spiral they are unable to escape. While there are many who like to point to The Process of the Philadelphia 76ers and use that as a template for future success, that is one example of relative success, while most other tank attempts result in nothing. Additionally, Philadelphia's process still has not resulted in the ultimate goal of winning a championship, and that is something that needs to be mentioned much more often. As tempting as tanking to potentially acquire high-end talent can be, more often than not, it results in nothing of consequence.