BuddyPress.org

I don’t know much but I think one nice option would be to comment out or remove the Blog creation details section from the register.php file of your theme.

register.php file residence : yourtheme/registration/register.php

blog creation details section on register.php would be approx : from line no. 169 to line no. 201

or simply comment out line no. 173
or the line with

<?php _e( 'Blog Details', 'buddypress' ) ……

and line no. 175
or the line with

<input type="checkbox" name="signup_with_blog" i …………………….

This may solve your issue with keeping the blog registration open but stopping new people from registering it from the register page of your site.