Should Greek write Tαβου instead of Tαμπου (for taboo) and Bιδεο instead of Bιντεο (video), as done in Cyprus?

A: no. 🙂 Transliteration reform has already happened in Greek, and it’s concentrated around simplifying vowels. No more omega for long o’s or eta for long i’s or <ai> for long e’s, as in Φλωμπέρ <Flōmper> = Flaubert, Σαίξπηρ <Saixpēr> = Shakespeare.

But at least those reforms have made phonological sense. This wouldn’t.

And B: I question the premiss. Cypriot stops work differently to Standard Greek stops: Standard Greek has a contrast of /(n)d/ ~ /t/ (ντ ~ τ), whereas Cypriot has a contrast of /nd/ ~ /t/ ~ /tʰ/ (ντ ~ τ ~ ττ). As a result, video and taboo are transliterated in Cyprus as βίτεο, ταπού <viteo, tapou>: <t> is considered there closer to /d/ than <nd> is.

Cypriot does not use βίδεο, ταπού: in Cyprus as in Greece, they would represent /viðeo, tavu/.

But that’s not because Cypriot is more rational than Standard Greek, with its <vinteo, tampou>: it’s because Cypriot is phonologically different, and is far enough from Greece to have its own transliteration norms, even if Standard Greek is the official language there. It’s also why Schubert in Cyprus is spelled Σιούπερτ <sjoupert> and not Σούμπερτ <soumpert>: <sj> = /ʃ/ in Cypriot.