Thea48

The XT3 would provide you with everything. You could use face detect for the street, have a ultra fast camera with the 35/2, 50/2 or 23/2 lenses and finally, this camera without lenses cost a few hundred dollars more than the X100F.

I think it's impossible compare the XT3 whit the others two cameras, simply because the size, so different. Sorry Steve, I don't think that "XT3 would provide you with everything". AndrewB if you "want to have the camera everywhere I go and you do a lot of street photography" with the XT3 you're going to have quite problems.
Cheers

Any reason why you aren’t considering the XT20? Seems it would tick all the boxes for you.

If you said you could afford two Fuji models, I would go with the X100F and the XT20 (don't overlook this option) or XT3. If you can only have one, and you wants as small a footprint as you can get while still having some lens options, I would go with the X-E3. If you are are certain that a 23mm (35mm fov on full frame) will suit the vast majority of your needs and you can only have one Fuji, I would go with the X100F.
The XT3 is the largest and certainly gets you away from the concept that the X100F and the XE3 provides. However, having owned all the models listed above, I don't find the XT3 to be as large as some articles and reviews suggest. I guess it is all in the feel of the beholder, but I was expecting a feel or experience that was significantly different than the XT20 and, while larger, I don't find it any more challenging or difficult or cumbersome to take the XT3 anywhere I took the XT20. But, as with all things, others may have a different impression.
X100F if you are absolutely certain 23mm is all you need and you like the retro rangefinder look XE3 if you want the smallest footprint that lets you change lenses. (XE3 is a sweet camera) XT3 (or XT20) if you want traditional SLR look and additional features at a cost 

My Ricoh grll is good for street photography, but I prefer my XT20 with the 27mm lens. Nobody sees me.

If you " want to have the camera everywhere I go "  and different focal lengths , you are looking for a very small foot-print with a zoom lens. I would say it has to get into a coat pocket and no extra accessory.
None of the actual Fuji cameras fit the bill.......and like you, I am waiting for Fuji to produce that camera.
So for the time being I am with another brand and  keep waiting.