I disagree. If a PC were Keeping Watch, they would be entitled to an active Perception roll, not a passive roll.
With this feat, for me the fun is when the passive Perception is higher than the active Perception...
So, there's no such thing as an "active roll." Or a "passive roll" for that matter. I think I know what you mean by those terms, but in order to wrap one's head around this, I believe using the proper terms is important. That's because it's easy to start thinking that a passive check is the mechanic used to resolve uncertainty when the character isn't actively doing something. And that's not how it works.
A passive check is just a special kind of ability check, used when the DM wants to resolve a task that is performed repeatedly (or if he or she wants to have a secret check for some reason). So that tells us that the character is doing something and, not only that, but doing that something over and over again which is certainly not being "passive." For example, Keeping Watch while traveling the adventure location. So if the DM thinks that Keeping Watch is the task of staying alert for monsters and traps, we use passive Perception to resolve any uncertainty as to whether the character is surprised by a lurking monster or notices a trap before it's too late. The player has essentially made a trade-off here: rather than perform any other task (repeatedly) that might provide a benefit of some kind, the character instead will be trying to avoid surprise and find any traps by Keeping Watch. And passive Perception is the mechanic that resolves both of those things, when they are uncertain.
A DM might call for a Wisdom (Perception) check - notice how I don't say an "active check" or "active roll" - when you take the Search action in combat or when you are not performing a task repeatedly, provided the outcome of the task is uncertain.
By its very nature, a passive Perception score will be lower than the result of a Wisdom (Perception) check about half the time. But those mechanics resolve uncertainty for essentially different tasks: the former is for tasks that are performed repeatedly and the latter for one-offs.