No. This is a misunderstanding of what CBT is about.
> But if something like "I screw up on X most of the time" or "I am in the bottom percentile for X" are statements that may occur to an analytical person that are objectively true and may directly cause negative emotions.
Okay.
> My understanding of CBT is that it suggests replacing these thoughts with positive forms like "sometimes I succeed at X" and "I'm better than most people at Y" (even if Y is something neither you nor anyone else cares about).
No.
Someone says "I screw up on X most of the time".
This is objectively true, and causes negative emotion.
Start with "What emotion do you feel?" Perhaps it's something like "shame" or "regret".
The therapist explores with you what your body is doing. When a person feels anxious their heart rate increases. Here's an important bit: try asking someone to slow down their heart rate - they can't. And it's the same if you ask someone to change a thought - they can't. The therapist will explain to you different physiological changes (sweating, breathing, heart rate, tense muscles, etc.) As you become aware of these things you can try breathing exercises to help ease tension.
Then ask what the hot thought is; what is the thought connected to "I screw up on X most of the time" that creates the feelings of shame? Perhaps the hot thought is "Other people get this, it should be really easy, I keep getting it wrong" or "I keep getting this wrong, and my team members have to keep correcting it for me, and it causes them more work and stress and tension".
You assign strengths to the emotions and to the hot thoughts.
You sit with them for a while - you're not trying to change anything yet.
And then, "I screw up on X most of the time"; well, can X be passed on to someone else who doesn't screw it up? Can someone give you extra help with X, or can they spend some time to teach you X? Notice that none of these are denying the reality of X. But now rather than worrying about stuff you can't change, you're giving yourself time to think about things you can change.
> So CBT is fine if your thoughts do not reflect reality but if they seem to encourage self-delusion.
I really fucking hate it when people condemn an evidence based effective cheap therapy based on misunderstanding and ignorance. Your attitude is causing harm to people who would benefit from CBT but who don't try it.