My take on it: (focussing on "why can't I")
Unfortunately any steps taken to stop the below also affects legitimate users. But, as mentioned in the other answers, these reputation limits are fairly low, so you should be able to easily get there by posting an answer or two (answers tend to be upvoted more than questions, assuming they're right and don't duplicate other answers).
By no means a complete list, but what I see as "the important stuff":
Why can't I upvote?
In order to prevent sock-puppets from serial-voting.
Why can't I comment?
In order to prevent spam commenting (and also presumably to reduce "thanks" and "great answer" comments, which should just be an upvote, not a comment, and for other reasons you shouldn't be commenting).
Posting has rate limiting (only allow a certain amount in a certain time frame) at low reputation, but commenting does not at any point (to my knowledge). With rate limiting, we can easily get spam accounts banned before they do too much damage.
Rate limiting on commenting wouldn't make all that much sense as sometimes you need to have a bit of back-and-forth in the comments.
And there's an automated ban for too many downvoted posts, without enough upvoted ones, while a ban stemming from too many flagged comments is likely manual (so we can stop spam accounts without manual moderator intervention, which is useful).
Why can't I upload image?
Imagine opening a post and seeing a completely offensive image (by whatever definition of 'offensive' you have). That won't be a very pleasant experience.
Now just stopping spam bots from doing this already helps.
Now words can also be offensive, but there may also be preventative measures for that, and you can just stop reading before the words do too much damage.
Why can't I post more than two hyperlinks at a time?
I'm not 100% sure on this one, but my guesses are:
It's too prevent posts that are too dependent on external resources by legitimate new users.
It's too prevent spam bots. Perhaps some just try to fill the post with links, so it prevents those.
Why can't I contribute answers to protected questions?
In order to prevent "thanks", "me too!" and spam answers from new users on high traffic questions. Keep in mind that most of these questions already have many answers, thus new answers are unlikely to contribute new information, but it's certainly possible that they will, so we just stop new users from posting them.
Why do I need 20 rep to talk in chat?
We can't allow anonymous participation on chat, so we require a small bit of parent site reputation to ensure that chat is reserved for active, engaged members of the community. (reference)
Keep in mind that Stack Exchange is a network of Q&A sites, not a network of chat sites, the focus is primarily on Q&A, being able to chat is just an added bonus.
Why do I need 5 rep to post on Meta?
Because we allow anonymous participation, we require a small bit of parent site reputation to prevent spam, and ensure that meta is for active, engaged members of the community. (reference)