It looks like you hide the groups with core workflow and this takes a moment. You should narrow down the visible groups in config → channels → web → group selection. If you only select one group here the user will not see the group field at all, if you hold the CTRL key you can select multiple groups the user is allowed to see. This works without delay.
Yes, I have checked this method too (btw, i wasn’t using Core Workflow to hide it) and right now using Core Workflow as workaround, but it’s still display all groups for a smaller amount of time. Like this: