Update: Works as of 8/8/21.
Go to chrome://settings/searchEngines
, hit F12 and paste this into the Console tab:
for (let el of document.querySelector("body > settings-ui")
.shadowRoot.querySelector("#main")
.shadowRoot.querySelector("settings-basic-page")
.shadowRoot.querySelector("#basicPage > settings-section.expanded > settings-search-page")
.shadowRoot.querySelector("#pages > settings-subpage > settings-search-engines-page")
.shadowRoot.querySelector("#otherEngines")
.shadowRoot.querySelectorAll(":scope settings-search-engine-entry"))
{ el.shadowRoot.querySelector("#delete").click(); }
NOTE: If you have more than a few custom search engines, you might need to run this more than once (press the up arrow in the console, and Enter again.)
You can also access the Javascript console via Option + Command + J on OSX.
Thanks to Mahmoud K. in the comments for providing a version of this, which I automated.