Making a reward for spending sats to make an NFT doesn't need another reward.

The reward is nobody else can use that private key to authenticate the name.

That's what the cost of a DNS record is based on, and why it is a speculative asset, and has been a form of savings for decades now (Mark Jeftovic has many stories as this was his thing).
Secondary markets are irrelevant to the base ledger. People wait days for domain name transfers currently. I doubt that waiting for a bitcoin confirmation is gonna be onerous.
Price discovery is in the remit of those operating the order books, it does not have to touch the chain at all, and we already have a type of NFT record, among several options that have existed since someone figured out you can put arbitrary data on chain with OP_RETURN.
And I'm pretty sure that robosats, and similar, don't have any blockchain behind them but function perfectly well as marketplaces. Neither would any market in Bitcoin NFT based DNS registration protocol.