Sure they "want" safe harbor protections because it's better not to be sued. But no, they don't "need" it as a platform really. Lacking that, they'd just start banning folks more aggressively to protect themselves.
Which, of course, is exactly what the president's supporters don't want, given his reliance on the platform. I mean, Trump literally (literally!) baselessly accused Joe Scarborough of murder last week. What do we think is going to happen if Twitter genuinely thinks they might be liable for the president's libel?
The cynical goal, obviously, is just to "hurt" twitter in the abstract, by making them look like a risky investment, drive off advertisers, etc... And that's why this is so distressing: here we have the president of the united states using the executive branch to attack a company simply because he's angry with him and not out of any kind of principle at all.