This separation has existed since the early days of Meta Stack Exchange being Meta Stack Overflow.
Even after the split, it's more a main site because Meta Stack Exchange doesn't have a corresponding Meta site associated with it (there's no Meta Meta Stack Exchange for example), and the formal "Stack Exchange" site is just the network landing page.
Interactions on this site should behave just like other main site interactions, because while the scope of the topics is different, most of the fundamentals do not radically diverge for that of any normal site.
Downvoting an answer should have an associated cost with it. If you're just able to do it for free, then you don't have any real gate or check on whether or not someone took the extra 10 seconds to panic about losing a unicorn point before clicking the button, or better yet, if they really felt like the answer was not that great.
Since some folks think this is more opinion more than informed conjecture, I've got some literature for y'all.
First, this is literally how downvotes work. You lose 1 reputation for downvotes and the poster loses 2. The rationale is clearly spelled out here by Jeff Atwood - you have to do something to stop people from going downvote-happy.
Quote of a quote inbound...
Please do something else to discourage downvoting. Maybe increase the cost to the downvoter (there’s already a “declined” on force user to comment on downvoting).
This isn’t about points. It’s about participation. Downvoting should be reserved for nasty/offensive/stupid/poorly-thought-out/totally-off-base comments. If someone spends the time to make an honest effort to answer a question, but it’s not that great an answer, just don’t upvote them… Downvoting sends a message, “We disapprove. You spent your valuable time, but we don’t care.” It makes me think, why should I bother spending the time to write up answers for this forum?
I stopped posting on several usenet newsgroups because the major participants were just nasty and sarcastic. Don’t let this happen to Stack Overflow.
[...] The problem isn’t downvotes, per se, but encouraging responsible downvoting.
So yes, from around the very beginning of the site, downvotes being at least not free was considered a key value of the network. Downvoting is still an important thing, and to be blunt, very few things in life that are important are free or should be taken for granted.
If you're too worried about losing reputation when downvoting, perhaps you shouldn't be downvoting.
Second, the original Meta Stack Overflow always had separate reputation from Stack Overflow, which was always unlike any meta site. This behavior was intentionally preserved as Meta Stack Exchange became its own site which serves its own role as a kind of catch-all arbitration ground for network-wide impacting things, such as themes, or generic discussions around things like Beta status or general questions about the network-at-large.
Not knowing this background about the network and wanting to insist that it change to suit your perception of what Meta sites are is short-sighted at best. While I won't deny that some of the company's decisions can make absolutely no sense, and can be incredibly arbitrary for no clear reason, if nothing else, the decision to penalize you for downvoting a question because you felt like it is still useful to prevent you from going completely unrestrained on downvoting questions because you didn't quite like its shape.
I mean, all it takes is for you to get a single upvote on a question or answer nowadays, and with that association bonus, you can downvote a whopping 11 answers.
This is not a hard hurdle to cross.
Don't make it seem that way.
To reply to some thoughts in the comments:
@Makoto I reviewed almost 4000 posts on another site. Why must I post here to be able to vote on the review announcement? Why would you even think to say that I'm "not participating". Or are you saying that in order to have influence about how reviewing works on the site where I review I must also give my time here. Posting what? Chat-chat posts about "What motives you to keep answering posts on your favorite site"? Those seems to get people lots of reputation points.. :O
There is not and never has been any magic bullet to address this concern. The thought of saying that someone who is well renowned in one part of the Internet automatically meaning that they can be successful or can contribute at a high level in another part of the Internet has always been a problem that the site has struggled with.
The blunt reality is that sites across the network - even if they feel similar - really are different. To get reputation on one site, you have to earn it. To earn it, you have to participate on the site you want to participate on.
I have heaps and heaps of reputation as well. Doesn't mean I'd be valuable as a reviewer on a site like Judaism or Chess because I wouldn't be as in-context to what everything is.
I don't see why having an opinion (disagreeing with a post) should result in a reputation removal. Considering here on Meta.SE, downvote typically means disagreement, not somewhere like SO or Anime.SE (or most SE sites in general) where downvotes imply a low quality or incorrect answer.
No one's taking your opinion away. Your opinion just doesn't get to be free, but it is at least inexpensive to express. Maybe this gets at the heart of "responsible" downvoting - I have an opinion on a lot these days and while I could downvote almost every answer, I've more or less matured to the degree that I prefer having sensible discourse and talking about why I disagree with something in a separate answer while also expressing how I really feel on a question or answer.