First downtube shifters, and to some extent barend shifters, are inaccessable if you are climbing standing and determine you need a lower gear in a hurry.
I'll buy less accessible, but not inaccessible. I guess it depends on how you set up the bike among other things, but I can shift just fine with bar ends while standing to climb.
I also do not find down tube shifters any less accessible than bar ends for me, but on the smallish frame I ride and with my preferred low bar position down tube shifters and bar end shifters are at almost exactly the same height and therefore the same amount of reach.
As I said I ride a smallish frame and prefer my bars 4-5" below saddle height, so riding seated or standing involves a good bit of bending at the waist any way. I acknowledge that someone who uses a more upright riding posture and or a larger frame would likely have a different take on this.
Not knocking STI brifters, I like them quite well, but I also enjoy riding my downtube shifter equipped bike just fine, even in the mountains.