I think it is definitely worth it (even 9 points). If you like doffing, then you can also get another 2,8 seconds, if you crit the battery mission (under personal). That should be a total of about 23 seconds your battery is working. You can also slot a maintenance duty officer to get the most out of using batteries (for additional effects).
Originally I skipped this altogether for all 3 classes.
Now I have it maxed out on my Engineers due to the class trait EPS Manifold Efficiency.
I still dont have any skill points spent in it for Tactical or Science, but since then I was able to get the RMC.
Is it worth it to spend the 9k in skill points in extending the duration of all batteries to 20 seconds (up from 10)?
Worth it for EPS Manifold Efficiency; assuming that you have an Engineering Captain who uses *TWO SETS* of EPTX powers on their ship (example: chain EPTS3, then EPTW1, then EPTS3, then EPTW1 - result is that an ability fires once every 15 seconds)
But I'd only take it to 3000, not max it out at 9000. (3000 gives +5 seconds duration, for 15 secs total... this means that when chaining two sets of EPTX abilities, EPS Manifold's buff will maintain 100% uptime.
IMO if the power bonus it grants is only up occasionally then you'll see little benefit from it unless you're willing to manually adjust your Energy Sliders every time it triggers. In which case, the Skillpoints (and trait slot in the case of EPS Manifold) can be better used elsewhere.
That said, I treat Capacitor abilities such as the Red Matter Capacitor or the Warp Core Capacitor powers as situational Emergency abilities, and tend to save them for when I need them (usually to bring a subsystem back online) rather than use them every time they're off cooldown. YMMV.
For my Engineers I put 9 points in it . . . that gives you 19.9 seconds for the duration for your batteries. Also, that gives you 19.9 seconds per cycle of EPS manifold efficiency. If you are chaining Emergency Powers, that gives you 39.8 seconds out of 60 seconds of +10 power to sub systems (not using Emergency powers). Also, the manifold efficiencies should overlap 4.9 seconds but I only get a sec or two.
Spec into batteries? YES YES YES. Quite possibly the best 9000 skill points you can spend.
Space combat is all about energy management, and batteries are free energy.
As you pointed out, having 9 points in batteries makes the power boost last 20 (19.9) seconds... and there are some warp/singularity cores that have a plus to BAT, giving you even more time... and on top of that there are DoFFs that give additional effects based on battery use.
So, yeah, with batteries you just can't go wrong. I've got the RMC, which is a big help... but I still eat weapons and aux batteries like they are candy.