Your suggestion that large companies ought to be "bound by law" implies regulations by the government. Whether or not that is your intention is still up in the air. However, if the government owns the regulation then they get to set the standards of what a big company is on a per criteria basis.
If the government is being attacked by a specific 'group', the government will then have the power to impose specific, targeted regulations on that group's web presence. Without the legislation, this is a matter of freedom of speech and is quickly resolved by the first amendment. It would be incredibly difficult to fight that off.
However, with legislation in place that affords the government the power to impose such regulations, they can quickly and most importantly (read terrifyingly) silence people on the web.
Platforms are not people. Regulating the way that companies offer their services, tax them, and how they are allowed to be structured is not a limitation of free speech.
We already do it with every other industry, social media only enjoys a lassaiz-faire regulation environment because of how new it is, the law hasn't caught up.
That doesn't imply that I 'trust the government'. I mean, trust is not binary. I trust politicians as far as I think that what they do fits their agenda. So I don't have any trust in 'the government' without context.
The reason why I think a law would be the appropriate solution is
- that the companies have no interest in changing anything towards an (e.g., privacy friendlier system) as it would endanger their market position and therefore their profits
- in the current situation, the majority of people has few alternatives, so they can't 'buy their facebook somewhere else'
- for new competitors, it is quite hard to compete even with a single product not to mention a whole set of them
So it doesn't look like the market will find a solution anytime soon. I am not a fan of too much regulation either. Many laws have problems addressing the real issue and take too long until their are changed appropriately, but most laws cause costs anyway (not just financially).
