(However, I imagine it would be appropriate on the supporter-only hosting forum.)

Unless you are Microsoft-sized, you probably don't need to literally lease nameservers. You'd have to be very, very big to need a dedicated server.

There are companies that provide third-party DNS service. They typically have a world-wide network of servers that handle hundreds or thousands of customer's domains.

This is similar to the type of service typically provided by a registrar, though generally with greater flexibility, reliability, and better customer service.

IMO, the most reliable of them use a technology called "IP Anycast", which puts multiple geographically-dispersed servers on each nameserver IP address. That certainly isn't a necessity for the average website, though.

You should expect to pay from $10-$20/year for DNS service for a single domain. Many services have fairly deep discounts for multiple domains, so it is possible to handle 50-100 domains for maybe $1/year per domain.

The very top tier - used by some of the highest traffic websites - can cost quite a bit more - $1000/month and up. They just don't want to deal with small-fry.

Just do a search for "DNS service" and you will find a bunch.