YES! but my 45 hits better be more accurate than that pic
In all seriousness I primarily carry 9mm for both my EDC and my "duty" load out. I do this for 2 main reasons, 1-Shot placement, and 2- capacity.
Shot placement means that effectiveness is all based on shot placement, whether you have a .45acp or a 9mm you will get similar results based upon where you place your rounds. Hits to the central nervous system, cardiac, pelvic area, will all yield similar results with a hit from either round. Likewise hits to non critical areas are no more likely to cause a "change in behavior" with one round over the other. That leads to #2
Capacity! If properly placed rounds are what is effective I want to have the maximum amount available. For instance my SA TRP in .45 carried 9 rounds with 8 ea in 2 spare mags for a total of 27 rds. My STI in 9mm carries 18 rounds with 17 ea in 2 spare mags for a total of 52 rounds. Hell I can carry just 1 spare STI mag and still have 8 more rounds than with my TRP. Even if you have a "high cap" .45 you are still generally limited to no more than 10. With my STI I have Mags that hold 22 rds without protruding awfully from the bottom of my grip. I generally carry these as my follow up mags. For my duty rig I only carry 2 spare pistol mags and I am still able to bring 62rds to the fight.
A third why is Follow Up shots. I find that shooting 9mm my 2nd and 3rd shots are faster and more accurate than when I shoot .45. Dont get me wrong, my TRP is accurate and if I was just worried about static qualifying I always defer to it, but for more dynamic shooting there is not doubt that I am more effective (faster and more accurate with #s 2 thru the end of the mag).
If you are fast and accurate with your .45 then by all means run the gun that you can get the best results with. This is just what works for me.
Chris