Adobe Illustrator is not able to vertically center editable text accurately. It would need to be able to align lettering based on its cap letter height in order to do the alignment correctly. Adobe Illustrator has never been able to do this and CorelDRAW can only do it within some serious limitations (typeface choice, letter choice).
In Illustrator you have to convert the text to outlines, up-group and/or release the compound of the text string and do a couple more steps in order to align the box and text properly.
Hiding the bounding box does not work. The alignment is still referenced to the bounding box around the letter regardless whether it is visible or not. If you're manually sizing letters, like making a Helvetica letter "H" 2 inches tall to later add some text to it the bounding box will be sized at 2" but the letter inside will be smaller.
I'm not sure if there is any rhyme or reason in how Illustrator sizes the bounding box around type objects that are not area type objects. I don't even know why the box is needed. The bounding box does not correspond to the size of a typeface's own built in font units box. For example, if I open Gotham Bold in Font Lab Studio 5, I can see its glyphs are designed in a 1000 unit tall box, ascender is 800, descender is -200, caps height is 700 and x-height is 536. If I make a 1" letter set in Gotham in Adobe Illustrator I might expect to get a letter that is .7" tall when converted to outlines. But I get a letter .6013" tall instead.
What is really needed is this: Adobe Illustrator must incorporate options to size, position and align type according to cap letter height. Sign making applications like Flexi can do this. Why not Illustrator? The program could read the built in info of any installed fonts and get that cap height data. I think CorelDRAW should be able to do this as well. I've made requests for this feature repeatedly at Adobe's Illustrator forum over the years and have also made the request at Corel's forums too. It doesn't seem like anyone in charge is listening.