A lot of this info shared is great. And aside from the regular maintenance as suggested by the owners manual really you don't have to do anything else if it's not causing a problem. Change timing chain now if it's not causing issues?? ok... I guess. $$ for what though. I've owned every gen of CTS and Gen 2 was the worst for timing chain issues, they even issued an extended warranty for all owners on the timing chain. Well I changed my oil every time on schedule and used a quality synthetic and after 11 years of owning my 2008 CTS I never had a timing chain issues that so many had. Take care of your car and if it's behaving good, let her be.
If you think 120K to 150K mile timing chains "don't cause issues" you don't understand the problem. Like a few parts on a car (shocks are a good example, control arms and other suspension parts are another) the degradation is slow, over a long period of time. Yet when you replace the worn part, the sudden improvement back to factory-designed performance is startling, revealing to the owner maintenance was needed and $$ was well-spent.
I'm assuming you already know the behavior of worn shocks and suspension. Worn timing chains cause slow response to VVT commands as slack is taken up, or even prevent the designed timing from being accomplished. This is indicated by hesitation at throttle tip-in and otherwise poor response. Fuel economy and power are diminished, and the loose chains are audibly heard through a faint rattle at high RPM, at start up, or even the extreme knocking indicated by a cam phaser that fails to lock in place at shutdown, whipping back and forth until oil pressure builds.
Like so many wear items on cars, the vast majority of drivers simply aren't perceptive enough to notice the slow deterioration. While it might be more obvious if it happened overnight, the slow progression makes it more difficult to identify. There is plenty of experience in the community with this engine. Even when well-maintained, timing chains eventually wear. The CEL light has been reprogrammed through a service update to software to minimize warranty claims by postponing the indication until wear is near-catastrophic, it is not to configured to indicate when wear has reached a level that is degrading performance.
All engines wear their timing chains, but it is particularly impactful to DOHC V engines with VVT. It is a common fallacy that timing belts need replacing and timing chains last "forever". Obviously this is impossible, and a large collective body of experience agrees.
If you have a high-mileage 3.6L V6 with the original timing chain and the CEL light has not lit (yet), I can assure you it is not "fine". All DOHC engines expected to run past 200K miles need a timing set replacement once in their lifetime.
If your Gen II CTS had 120K to 150K miles when you sold it, you can be sure it had timing chain issues. You just didn't address them.