When it comes to email deliverability, the physical location of the DNS (whether it’s on the host server or the domain registrar) is not the primary factor. Instead, the accuracy and completeness of the DNS records related to email are more critical.

However, there are some nuances and reasons why one might choose to have DNS on their host server rather than their domain registrar:

1. Centralization: Hosting DNS on the host server (especially if you’re using a hosting provider that integrates web and email hosting) often means easier management. You have everything in one place, and the host may auto-configure certain records, making it easier for beginners.
2. Automatic Configuration: Some hosting providers offer automatic configuration of necessary email DNS records like MX, SPF, DKIM, and DMARC if you host your DNS with them. This can reduce potential configuration errors.
3. Speed: In some cases, if you’re using a hosting provider’s nameservers, changes might propagate faster within their internal network. However, this speed difference is generally minimal and not a primary reason to choose one over the other.
4. Support: If you’re not technically inclined, having your DNS with your hosting provider might be advantageous. This is because if any issues arise with your website or email, there’s only one support team to deal with.

That said, regarding email deliverability, the most important things are:

1. Correct DNS Configuration: Ensure that your MX records are set up correctly, pointing to the right mail server. Also, it’s essential to set up SPF, DKIM, and DMARC records, as these help verify the authenticity of your emails, which can improve deliverability.
2. Server Reputation: Ensure that your email server’s IP is not blacklisted. Using shared hosting can sometimes affect this if someone else on the same server sends spam. Dedicated IPs or reputable email providers can help.
3. Content and Behavior: Sending high-quality content, ensuring opt-in methods for your mailing lists, and respecting unsubscribe requests are critical. Avoiding spammy behavior will help maintain a good sending reputation.

In conclusion, while hosting your DNS on the host server can offer convenience, it’s not the primary determinant of email deliverability. What’s more important is to ensure correct DNS configurations, maintain a good server reputation, and engage in best practices when sending emails. If you’re unsure, it might be worth consulting with your hosting provider or an IT professional to make sure everything is set up for optimal deliverability.