As above, https://wordpress.stackexchange.com/a/195673/22728 solved it:
add_filter( 'wp_kses_allowed_html', function ( $allowedposttags, $context ) {
if ( $context == 'post' ) {
$allowedposttags['input']['value'] = 1;
}
return $allowedposttags;
}, 10, 2 );