One reason is that integrated shifters' cables tend to interfere with a handlebar bag. That's probably becoming less of an issue however as more of them put the cables under the bar tape.
Another reason is that integrated shifters have had the reputation for breaking down much more easily. That reputation may have been justified at one time, but today STIs last last tens of thousands of miles, and most of the malfunctions require no actual repair or replacement but can be corrected simply by cleaning. That can be a problem on tour though. One of the STI-equipped bikes in our family needs it about every thousand miles or even more often. Another one has only needed it two or three times in 10,000 miles. Another one has had no trouble at all in its 16,000 miles.
When an STI shifter has the problem, it gets to where the shorter lever acts like it is no longer connected inside. I take the LPS-1 aerosol can with a tiny straw, open the brakes' quick releases so the levers can be pulled in farther, and spray the penetrant/lube into the inside of the shift mechanism. While it's saturated and dripping (actually I use rags to keep it from running down the handlebar or onto the front wheel and tire), I pedal the bike on the little stand and work the shifter up and down the range many times, and repeat. It only takes a few seconds to make a totally non-op shifter work absolutely like new again. It is not necessary to remove the shifter from the handlebar. LPS-1 leaves a dry lubricating film, so it doesn't attract road dirt. The shifter mechanism resides in kind of a cylinder in the lever housing, and there's a hole in the side, near the front, where the cable is fed through during installation. I put the straw into that hole and aim it back toward the inside of the mechanism. The LPS-1 comes out foamy and this foam fills the whole mechanism.
I should probably mention that we did have a bar-end shifter go down at maybe 4,000 miles a couple of years ago, although that's probably extremely rare too. The indexing ring broke and was sticking out from under the plastic cap. IOW, bar-end shifters are not immune to breakdown either. But even with the broken indexing ring, the bar-end shifter was still usable in friction mode, unlike a non-op STI shifter.
I mostly ride on the aerobars now myself though, even all day, so I put the bar-end shifters on the aerobars, and I don't expect to ever buy STI again. The same goes for our two sons. Our bikes with STI don't get ridden much anymore. Having shifters on the brake levers has been around at least since 1949 but hasn't been popular until the last 15 years or so. If fit correctly (which most aren't), half of aerobars' value is comfort. They offer a lot of relief for wrists, elbows, shoulders, and other parts. I have very small bones and joints for a 170-pound man, and even as a teenager in the 1970's, the pounding from bad roads quickly left my wrists and elbows in pain. That trouble ended ten years ago when I got aerobars.
If it matters to you, bar-end shifters and separate brake levers are both lighter and a lot cheaper than integrated shifters.