I agree that makes sense, but it makes potential subscribers to the third parties nervous. I like Kagi Assistant because my payment is capped.
I get nervous plugging my pay-as-you-go API keys into random software because of the risk they rack up a $1000 bill doing something I wouldn’t have paid $20 for them to do.
The other three things are that economies of scale make it cheaper for Kagi to buy a bajillion tokens, Google et al don’t want to manage the customer side of things (what service ate how many tokens?), and service providers don’t want you seeing their “magic” in your console. Seems like there’s a lot of power in the system instruction side of things, and Perplexity probably doesn’t want you seeing their prompt.