There's no need to create a graphic style first to do this, you just need to apply the appearance to the Type and not the Characters in the Appearance panel (which is what happens when applying a graphic style). Then you can drag the stroke beneath the fill, and add additional strokes if desired. Technically the stroke is still being aligned center, but now it's not cutting into the fill.

You CAN have inner & outer strokes on text if you apply a graphic style to your text first. Once you have the inner & outer strokes available, you can create additional inner & outer aligned strokes. I created a graphic style by making a simple shape with 3 strokes - an inside, an outside and a center stroke. I made them each a different color and moved the center stroke to the top (not essential to do - it's just to make them easier to see - my personal preference). Create your new style using this shape. You can apply this style to your text and your text will have all 3 types of strokes. If you want to add additional strokes, in the appearance panel just select the stroke that has the type you want and either drag it down onto the new icon to duplicate it or just click on the new icon and the new stroke will have the same alignment as the one previously selected. Turn off the visibility on any strokes that you don't need. You could delete them, but I would suggest just leaving them so that they're available for future editing. Clearly this proves that text CAN have strokes aligned to the inside or the outside of the path, so WHY do we have to jump through this extra hoop in order to do it? We should be able to change the stroke alignment directly on the text in the first place.

Yes! Please please please add this. The workarounds are so annoying. I don't understand aligning stroke to outside isn't possible, what gives?!

I made the leap to Illustrator after many years using CorelDRAW, and this feature is one of maybe six that I still miss.

I'm surprised this doesn't have more traction. I would argue that one of the most important features of Illustrator is maintaining editability. Why should we have to outline our text in order to use stroke alignment? It makes no sense to hinder a feature this way.

Maybe I use Illustrator in a way that is outside of the norm, but I wish I could add more weight to my vote. I would think logo designers would be all over this feature request.

@Dan Changing the order of the stroke in the Appearance panel does not enable stroke alignment--at least not in Illustrator 22.0.1.

You can actually do this by moving the stroke below the characters in the appearance panel. Although it can be quite buggy.

Also! I don't understand why aligning strokes don't work for open paths. I have to build custom width profile to simulate this — 0 at on side, full width on the other. Why? You think that people will be angry, when outside will look like inside, because of path direction? Make a button for changing it to Stroke palette already.