can it be done? if not, why?

SHA-1 is used for BitTorrent v1, and SHA-256 for BitTorrent v2. As far as I know, SHA-3 still has no use in BitTorrent. It's not the choice of Tixati developers, it's just how the protocol works. But, if you want to generate SHA-3 checksums for finished downloads, you can use Teracopy for example.

Clarification: the SHA-256 algorithm is used but cut off at the length of a regular SHA-1 hash. 160 bits?

The v2 hash generated by Tixati and qBittorrent is uncut for both v2 and hybrid torrents. But, according to libTorrent blog, DHT- and tracker announces and lookups for v2 torrents, use the SHA-256 info-hash truncated.  

Thank you, TX007. I thought this applied everywhere.