Should every bot be allowed?

Allow the crawlers you want to be able to cite you. You can still block bots that only copy the site and never send a visitor.

Does a sitemap replace crawler access?

No. A sitemap lists URLs. The crawler still has to be able to read each one.

How do AI crawlers affect brand visibility?

If an AI crawler cannot read a page, the assistant cannot cite it. robots.txt is not the only gate. A firewall, a CDN rule, or a login wall can block the crawler even when the file looks open. Visibility starts with a page the assistant is allowed to fetch.