Sorry, but I could no help this one. Reading of STI 5600 / R700 manual (disclaimer notes):
https://si.shimano.com/pdfs/si/SI-6KD0C-002-ENG.pdf

"Use a [sic] frame with internal cable routing is strongly discouraged as it has tendencies to impair the SIS shifting function due to its high cable resistance."

Since, Shimano moved on to the concealed cable housing for not only brakes but also shifting and introduced the right angle kink to the shifting cable right in the lever, also there's no mention on the internal cable routing at all (4700-9000):
https://si.shimano.com/pdfs/dm/DM-ST0002-05-ENG.pdf

So, what has changed since? Are the cable housings space tech now?

Don't worry about it.

I knew it.

Xanax

Newer 10 (Tiagra 4700) and 11-speed shifters pull more cable per gear shift, compared to the 5600 / 5700 10-speed shifters.
This provides a bit greater margin for error, making the system a bit less sensitive to any cable and housing imperfections.

Not that I'm a fan of internally routed cables - quite the contrary.

IME, one of the issues with internal routing is the micro housing/sleeve that encases the cable going through the interior of the frame has a tendency to get kinks in it. I have one bike that has internal routing, I finally got it to shift correctly after re-doing all the cables and housing, using a sleeve for the cable that is a bit more flexible, black replaced white/clear, making sure the cable/housing was lightly lubed with oil, and minimizing the angles in the routing. I am positive that the routing was poorly done by the shop the bike was purchased from. I bought the bike online from a shop 3,000 miles away, so having them do the re-routing was not an option. I did buy a Park Tool routing tool kit, and it helped, but I am pretty sure it can be done without it.

For transparency, I was not at all familiar with interior routing and it took me quite a while to get tired of constant adjustment of the shifting. Between watching videos and my LBS, they gave me the different sleeve, the re-routing was a success and I have had no more shifting issues since. This is a CF frameset, and do still get some low level rattling from the cables going through the down tube. I am not in the market for a bike, but I likely would not get another with internal routing.

This was a 2014 model that I purchased new in 2016. From what I have read and seen, the performance of this routing has been considerably improved.

From what I have had to deal with today's housing/cables with materially lower friction have made a huge difference over yesteryear's cables.

My bike has internally routed cable and the shifting seems OK, especially after I installed new shifter cables.

My guess is that the design of the bottom bracket shift cable guide is key to shifting performance. The one on my bike has large and gentle bends for the cable compared to some others which I have seen in these forums. But the guide has to be removed to thread either shift cable through the guide, and both cables have to be removed to remove the guide, so the design essentially forces me to replace both cables at the same time.