CoD or not, it could be fun - I also hate completely shutting down an idea before at least discussing it. Not sure I like the morale system, seems to needlessly complicate what could be a simple but fun game mode.
I'd say three points maximum, all with double the standard cap rate. There should be a set time limit and no point cap. A ballpark figure could be twenty minutes (possibly more) to not break attention spans too hard and it is tried, tested and functional as the competitive time limit. Points are gained passively by holding a point, the more you own, the faster you gain points. So locking down one point completely won't serve you much benefit. Points can also be gained actively through kills, the standard 13 we see in current KotH and CK matches.
Okay, so to prevent the last ten minutes of the game being ragequit city when it becomes impossible to overtake the amount of points gained by one team, there should be a system. Owning two of the three points grants a ninety second (subject to change) countdown to a win condition for the team in possession. Owning all three at a given time should give a thirty second win condition.
Additionally, an overtime mechanic would be beneficial. I'd say that, if a team holds two of the three points and enters the ninety/thirty second win timers, the match can extend beyond the time limit unless said team is currently ahead in points. Also, the ninety second/thirty second timers should be frozen when a point is contested. Unsure of whether this should be while a point is being decapped or whether an enemy is in the cap zone at all. Given how harsh ninety seconds is in a game where getting from A to B can take just as long, I propose the timer should be paused if an enemy ship is being registered in the cap zone at any point.
A rough draft, derivative from your idea.