-------- Yes -you are shorting a part of the winding but the switching is a bit more complex than that so that short circuit currents are limited to reasonable values. It is a multistep operation with reactor switching. On-load tap changers are expensive and are generally limited to applications where this is absolutely needed (I have seen one where the tap changer was nearly as large as the transformer).
--------------
------------- Possibly but probably not- I am out of date on this but I would expect that the old way of good switches plus reactors might still be the better way. It saves a lot of control wiring plus a lot of money to operate thyristors at
300KV and 500A or more and I doubt whether they would be cost effective or technically advantageous otherwise. --------------------------"on load tap changers"? Not likely. These were applied to transformers only where it was worth the effort. Definitely transformers in rural areas- typical pole pigs- would have to be de-energized as the tap changer is a manually operated switch inside the tank. Some larger transformers did have off-load but live changers operated from ground level. What you saw could have been somethng else altogether. Delta primaries as you indicate were around when you were a kid, would, in most areas mean that you are now a pensioner. I remember cases of conversion from delta to star for distribution primaries in small towns being done about 60 years ago and use of delta for transmission died much before that.