Yes you can trade on computershare however they are not a brokerage and their fees are astronomically higher compared to any main stream broker. Because that’s how they make their money. It’s much more economical to purchase from a main stream broker and then transfer your shares over, it’s very easy to do.

I purchased mine with TDA as well, just gave them a call told them to do an outbound DRS transfer, they ask you which stock and they take care of everything. In fact the lady I spoke with made the comment “oh yes, we have been doing a lot of that one lately“.