Social media can and does have both.

The whole point of Section 230 immunity is to basically neutralize the platform's responsibility so in that case they shouldn't care who says what and let the opposing sides battle each other on the merits of what's being said.

So why do they maintain huge and cumbersome speech codes and rules of what can be said on their platforms?

It's simple. Threat of regulation. The tech monopolists are like the old time robber barons of the early 20th century with their mega corps (railroads, oil, tobacco, etc). They are trying to hang on to their behemoths' power and appease political forces at the same time.