The only advantage to carrying two rods is to the person who finds the 2nd rod that you forgot or lost in the woods... 😉
I would NEVER carry two rods because in my entire life, I have never encountered a situation where I felt a quick change of equipment would present enough of an advantage to justify the hassle. I have on one or two occasions walked back to the car to swap rods, sometimes going from fly to spinning or vice versa, but that was more for fun than gaining an advantage.
IF we are NOT talking about carrying a traditional outfit PLUS a specific tight-lining rig:
In regards to a need for different line weights for finesse; the ONLY time I use light line rods on most streams is when I am relatively positive I won't be throwing heavy or bulky stuff for a pronged period. If I'm fishing a really small stream where a short rod is my preference, it will also be a light line rod because all of my shortest rods (5'0" - 6'6") are 3wts with one 4wt in the mix.
If I am not sure about the heavy/bulky thing and I'm not fishing small water, I grab a 5wt or 6wt rod because in my hands there is nothing I can't do with a 5wt or 6wt when it comes to 99% of trout fishing situations. That's NOT something I can say about a 3wt...
I guess I'm old school, but the thought of throwing size 20 BWO's or smaller stuff with a 5wt or 6wt outfit doesn't terrify me OR the fish. I get all the finesse, stealth and "tactical" (I hate that word applied to fishing) advantage I need by tweaking my leader & presentation.
FWIW - My go outfit on the Letort for decades was an 8'6" 6wt and I have never fished anything lighter than a 5wt on the Letort or Big Springs in my entire life. If those fish can deal with 5wts & 6wts, any fish can...