If you were standing at the entrance of a grand amusement park, would you feel despair that you have to choose which ride to take or excitement at having options? If the park were fantastically more grand, so you have no hope of sampling every amusement, does this somehow change your response? Your emotional valence here is your choice, not something intrinsic to the setting. That is what those cognitive behavioral therapists are trying to help with. But, they have to come up with some actionable instruction to convey it to us. I think you are arguing against the chosen rhetorical device rather than an actual principle.

Whether it is rarefied academic pursuits, music and arts appreciation, friendships, love, delicious food, sex, or ... we have to decline a world of countless possibilities to engage what is in front of us. And even then, we need rest periods in order to fully appreciate those rare few branches we do take. You can't enjoy or pursue anything 24x7. The nature of our experience is inexorably tied to the exclusion of other non-experiences.

In other words, life is a constant stream of decisions and branching points. The underlying angst of "not enough lifetime" is rooted, I think, in grief for these other paths not taken, for the loss of imagined alternatives. This is supported by the delusional idea that we could defer and return to every branch (given enough time). It ignores the ephemeral and limited nature of most opportunities and potential experiences, the necessity of closing one door to open another, and that most doors are never open to us (individually) to begin with.

You wouldn't just need a hundred lives or a thousand years but some kind of combinatoric explosion of a Multiverse You, where you could explore every choice of collapsing decision point. But what does that even mean? I think it's another delusion about identity and the self to think that "you" can experience the different paths. You'd be many someones else. If you could somehow fuse them together into an experience, you've just added some kind of sci-fi "hive mind" to your experience. But wouldn't you wish you could have experienced those things as an individual...?

To get stuck with this frustration is a failure to mourn. A failure to accept a finite life and get on with it. That leaves the grief stuck in the back of the mind. This is where philosophers of mind might tell you about desires as the source of suffering, etc. Where practitioners might propose moderation or the so-called middle path. Where the CBT folks might say you are on the path so you might as well learn to enjoy it, and offer a grab bag of tricks to help achieve that.