its not necessary to go through all pins. jtag has a number of commands. there are general commands and device specific commands.
in a chain, after powerup, you would first send the command to identify how many devices are on the bus. (basically you send in a single logic 1 and clock. count the number of clockticks before the one comes back out. that the number of devices. then send the identify command. each device will send out manufacturer and part number.
then you can tell individual devices to temporarily go in 'bypass'. meaning they pull their chain out of the loop and short their tdi and tdo together. that is how you speed up since you don't need to race through those shifters.
there are even ttl chips with jtag. there is an equivalent of a 74245 with 4 jtag pins. this allows you to inject such a device in a critical pathway on a complex board and ease testing.
or , using a little adapter board, temporarily remove the 74245 and pop the jtag version in. hook up the jtag dongle to the little adapter board and bob's your uncle.
74bct8245 is such a part. there is a whole family of em
http://www.ti.com/lsds/ti/logic/boundary-scan-jtag-logic-products.pagenow, before you get all excited and think about building your own superduper jtag tool : most of the information pertaining to guts of the devices are secret. some manufacturer specify some of the codes (the comon ones as mandated by the standard,but some of the advanced stuff is under NDA ...
therefore the JTAG probes with that fancy software that dave showed cost $$$