I remember doing something like this for VX ACE some time ago, I don't know well how it behaves in MV. The message system should trigger the opening animation only at beginning of text and closing animation at the end.
So if your event has text, text, text, there should be only one opening and closing animation (no animation between texts). And if you you disable those animations you shouldn't see the animations at beginning and end (and the pause between texts).
Now the problem is when in your event you put something between those texts, like a choice or a change in switchs, etc (don't know well which ones). Then suddenly those opening and closing animations appear (the message window is being disposed and created anew), and that's what you are seeing.
Then, solutions for that would be, without plugins, to discern what makes the animations trigger between text, and avoid them. Or make a plugin that accepts script calls that force the system to not dispose of the message window, and you manually call it at the begging of a text scene and at the end.