[Nisgeis]

JT sonar, the replacement for JP sonar gear in mid 1945 could be driven from the TDC. It had an indicator showing whether the target was to the right or left of the bearing it was trained on, so you could easily see if the target was lagging or leading the generated bearing and so check accuracy. It was very accurate as well, about 2 degrees if I remember right. So the technology was there to have the periscope aligned to the projected bearing from the TDC, it probably wasn't implemented as the sonar would have been used continuously, whilst the periscope only once in a while, so the need to have it track wasn't there.

Skippers didn't like exposing their periscope and minimised the time it was up. It takes a while to operate the stadimeter for example as you have to wind things into place. Using the horizontal stadimeter takes even longer to get an AoB measurement and was hardly ever used. Automatic periscope training was probably a cost that wasn't deemed warranted, or maybe it would have taken time to engage/disengage... not the sort of thing you want when you want to get a bearing and then take a quick sweep for escorts.