A lot of the gains one would experience with an interior vertical are negated by the introduction of two additional 90 degree bends (which would then have to be reclaimed by a higher chimney, so even more colder, slower to heat up temperature decreasing by distance....).
Obviously the question will be a moot point if the building codes don't allow it, but there are many reasons why most would avoid it (by the way, my installation is direct rear exit).
The ideal, of course, is straight up interior, anything else is a restriction to some degree or other.
Having a horizontal direct outlet locks one into a specific stove or exit height that should the stove have to be replaced it would have to be identical, a smaller stove on a raised hearth or a total reconfiguration of the wall thimble.
Some codes (or accepted methods) would say that one has to have the ability to disconnect from or access the chimney without having to move the stove (mine is on thick furniture moving pads, it can be slid out easy enough across a polished marble tile floor that is the hearth).
Going right into a chimney could introduce some issues such as clearance to the stove collar, possibly a higher temperature for passing through the wall either by being closer to the stove (though that would be an aid to the exterior part of the chimney) or any additional heat transmitted to the outer layer of the chimney pipe (I keep a magnetic thermometer on the exposed portion of the horizontal chimney pipe before it enters the wall, so far I have not seen temperatures of any concern, but then again, my stove has an insulated back).
The idea that going vertical as quickly as possible increases the draw (though as I first said, I do question the effectiveness when adding two additional restrictions, and for me, my stove already bucks that rationality by exhaust going horizontally within my stove plus fully through a downdraught when the bypass is closed).
As for the connection, I use a 6T/DSP-CPA to connect to my chimney (selkirk ultra/sure temp) which is a short connector.
For me, I live in an area where building codes and inspections are at best the realm of banks issuing mortgages or how stringent insurance underwriters are, which means I made my choices on my best efforts of researching available materials and guides, and balancing common sense and risk management with what I wanted to accomplish, what I wanted to avoid, and the space in which I had to work with and/or wished not to change. The safest answer, of course, would be to have no stove (or heating appliance) at all, but since that would entail living in the tropics, it's a matter of doing your best to over-engineer and minimise risks, and hopefully I was able to do that with my situation and the choices I allowed my self to make. In the absence of codes or rules that would say you can not direct exit, you would have to do the same evaluation of pros and cons while maintaining as much safety as possible. The most effective chimney is the most direct, but is it the best in all circumstances, that part I certainly can not answer, especially since every situation is unique in one way or another.
