Not in this case: this is a tender offer, and what you're describing is a merger. Which might actually make sense, but it would be something that goes through the TSLA board, and can't be done unilaterally by Musk.

Of course, he must be supremely influential with the board, but there is a governance structure that can't just be bypassed.

If TWTR holders want to trade for TSLA they can simply do it on the open market

When you see "Acquired for 50% cash and 50% stock" this is a company "trading" x shares for y shares. So yeah this happens all the time not in the open market.

Not for the premium he's offering to take it private.

This is true. But if he was talking about trading shares of SpaceX for TWTR I would probably rearrange my holdings.