I hate to jump onto my soapbox, but feel there is a lot of fear, misinformation, or lack of knowledge, that may be influencing some of the responses.
a) U-joint and drive line angle are usually (if you buy the right kits) adjusted and sometimes create better angles then those from the factory
b) The corrected steering geometry and longer control arms have better effect on handling and less jarring ride than the factory suspension
c) New springs with custom or even progressive spring rates are available as well as adjustable, or just pain better, shocks than offered by the factory
d) Newer kits allow for better joints (most of the time rebuildable, or at least poly vs. factory rubber) and stronger material
e) The OP never gave details about the type of kit they were looking into, and at the end of the day it is their responsibility to take all the details into consideration and buy the kit right for the intended use. E. G. you wouldn't buy a desert race kit of you were primarily towing or street driving.
I agree with all the concerns, however a lot of those concerns have been addressed by some of the better lift kit manufacturers over the years. If the OP plans to just slap on some generic lift blocks and spring spacers, then heck no I wouldn't recommend towing with that truck, but anyone that does that wouldn't even like driving their truck with how bad it will feel. A truly engineered lift kit, designed for a specific truck and use that takes driveline angle (both front and rear), steering geometry, higher grade components than stock, and ride comfort and control into consideration, I wouldn't hesitate to tow with it as I currently do... Heck, even my father-in-law who sometimes co-drives with me on a couple family trips thinks my truck is a better towing vehicle than anything he has driven.
I have gone cross country (towing multiple trailers) 4 different times, it has taken some trial and error to see and feel what works best for my comfort, and mine is a completely custom lift not just and off the shelf kit. Yes, it started with off the shelf components, then off the shelf components from other manufacturers put into the mix, then over time when I didn't like something, I upgraded it for the intended purpose that I use the truck for.
The following is not a guide, just shows my path/experience:
1) Started with an off the shelf short arm (read cheaper end of the spectrum) BDS 6" lift and 37" tires --- Looked great but wasn't happy with the driving and too bouncy/soft in the rear when towing
2) Added an aftermarket steering box and upgraded the steering component for a better geometry, and now my truck has a better turning radius than any other truck I've driven, despite the lift and larger tires.
3) Added airbags to the rear to help when towing, needed to get spacer blocks for them to fit as intended.
4) Changed shocks about 4 times till I found ones that helped ride the way I wanted and maintained comfort, the last setup I have custom upper shock mounts built that used eye mounted shock (similar to most rear shock setups) rather than the factory screw top/sandwiched rubber bushing combo.
5) Upgraded the front springs, but they are a little too hard and might change them again, going with a custom progressive rate
6) I have recently, last fall, downsized my tires to 35" but only in the effort to get a more level towing configuration with the 5er
Still on my to-do list --- Longer arms in the front, to better help front driveline geometry/angle, it isn't a problem now since I have the manual locking hubs and no longer feel the vibration on the highway, but the long arms will help that as well as will be less jarring on bumps. The shorter arms jam the arms into the chassis just due their angle and an upward force of a bump goes up the arm more than up into the spring, longer arms allows the spring to absorb the bumps more than the arm/chassis joint.
So as my truck currently sits now:
6" lift
35" tires
Air bags
09+ front steering setup
Borgeson steering box
Steering box support
Bilstein shocks
Custom from shock mount for eye style upper shock mounting
Upgraded driveline U-joints
Manually locking hubs with rebuildable bearings
pics can be seen here: most are with the 37" tires one with the 35" tires
//heartlandowners.org/showthread.php/50023-Show-off-your-towing-rig!?p=401121&viewfull=1#post401121
Now, my final comment... I'm thinking about upgrading trucks at some point, since the kids are getting bigger the mega cab might be in our future. But, I will never get near what I have put into my truck back out of it, and it has been tuned to my liking over the past 6-7 years of owning it. I made it the perfect truck for me, not for trade-in value or resale. My biggest fear about getting another truck is that I won't like it as much as this one, only second to that is that I have spent more on this one than a newer one costs, but trade-in value is half, lol... Just keep that in mind when thinking about upgrades...