As with everything business related, the answer to this question is like the answer to 99 out of 100 questions. Money.
By having you apply for a new card, you'll then have an additional product in your wallet. 2 products is better than 1 from the creditor perspective, as the only possibility is that you'll spend more if you have 2. You certainly won't spend less. Second, most people tend to use a new card more than an old account. By handing you a CLI on an old account, sure you may use the old card a little bit more. However, if you take on a new account people tend to favor their new card for a while, be it 6 months, maybe longer. Naturally, CCCs will benefit from this increased usage.
Where they fall short with this practice is when people like me call their bluff. I've had a Capital One QS that's been stuck at a low limit for over a year now. I used to throw $2k/mo through the card back when it was my daily driver. They wouldn't give me any CLIs, but all of my other cards were and I was also picking up new cards along the way. My newer cards took on my spend, to the point where the Capital One card has been in my SD for probably 6 months now. Had they given me a CLI back when I wanted it, I probably would have continued using their card and possibly apped for 1 or 2 less cards that now get more of my spend since I have them.
