A cache shared by a couple thousand people would have lots of stuff already cached. Running your own would be add latency as you'd need to fully resolve more domains.
Only on initial use. Most DNS records have a cache time of 24 hours, so if you're using the internet every day, you're unlikely to notice.
Some latency when visiting a new site seems like a small price to pay for side-stepping all the shenanigans that ISPs have been doing to DNS, without having to defer trust to yet another cloud provider.
