Set the Edit xProfile Subnav as the default one for self users xProfile nav.

bp-custom.php

<?php
// Exit if accessed directly
defined( 'ABSPATH' ) || exit;

function eloyruiz_edit_view_as_default_subnav() {
    $bp = buddypress();

    // Make sure other users than the current one will get the public view
    if ( ! bp_is_my_profile() ) {
        return;
    }

    // Edit the main nav to use the Edit subnav as default.
    $bp->members->nav->edit_nav( array(
        'link'                => sprintf( '%1$s%2$s%3$s',
            trailingslashit( bp_loggedin_user_domain() ),
            trailingslashit( bp_get_profile_slug() ),
            'edit'
        ),
        'screen_function'     => 'xprofile_screen_edit_profile',
        'default_subnav_slug' => 'edit',
    ), 'profile' );

    // Remove the public nav.
    $bp->members->nav->delete_nav( 'public', 'profile' );
}
add_action( 'bp_xprofile_setup_nav', 'eloyruiz_edit_view_as_default_subnav' );