Various websites discriminate against users of Firefox's private browsing mode, such as T-mobile. These websites block access if you're in private browsing mode.
There's an addon called "Hide Private Mode" that modifies Firefox's exposed state to prevent detection of private browsing mode, to solve the original problem. However, on the addon page it reads, "This add-on is not actively monitored for security by Mozilla. Make sure you trust it before installing." Most users are not going to have the time or capability of properly vetting this addon against it's current behavior or future changes. So, the risk is likely too high for most users for a computer used for work, banking, etc.
Therefore, the request is to pull the feature into Firefox core, perhaps controlled by an about:config flag, so that there's no additional trust or vetting needed. I would argue that, by default, private browsing mode should be undetectable, to prevent discrimination against its users.