Can I send emails from WordPress without external services?

The short answer: yes. WordPress ships with wp_mail() and sends emails without any external service:

wp_mail( $to, $subject, $html, array(
  'Content-Type: text/html; charset=UTF-8',
) );

The problem: deliverability

From shared hosting, those emails usually lack aligned SPF/DKIM and end up in the spam folder (or bounce outright). For the odd notification to your own inbox it might do; for emails to users, it’s not reliable.

The recommendation

Use a transactional service like Resend with a verified subdomain (for example em.yourdomain.com). Delivery improves enormously and you protect your domain’s reputation. The ideal setup: the form uses Resend if it’s configured, and if not, falls back to wp_mail as a safety net.