NAT Gateway can be shared via VPC peering

You can't (easily) share a NAT Gateway between peered VPCs.

You can do it by placing a proxy server in the VPC with the shared NAT Gateway - but then you have to configure that proxy server on everything in the VPC without the NAT Gateway which may be inconvenient (at best) or impossible (at worst - if applications don't support the proxy).

You can share a NAT Gateway by using Transit Gateway to connect the VPCs together. However, that adds extra cost (perhaps more than you are saving by removing a NAT Gateway). For more than two VPCs this could be a viable option-wise.