By using MIT for contributions, there’s no issues with relicensing them later.

IANAL, however, I'm pretty sure that software released under the MIT license can't be relicensed. The MIT license may be may be exceptionally permissive, but you are not given the right to license the contributed works under any other license terms.

Please review the text of the MIT license. Not only is it allowed, it's allowed explicitly. This is why FSF, for example, is okay with MIT, and so are many corporate shops: If someone forks an MIT licensed project, the forker is allowed to make all the fork's releases available under some other non-MIT license. In the case of copyleft proponents, this can be some reciprocal license like GPL. In the case of someone doing commercial closed source, this can be some non-free license that doesn't require offering the source to recipients.

Sorry, I must be not getting something, but I'm reading MIT (Expat) license's text and I don't see this.

On the contrary, it says that the copyright notice (= the license) shall be included in all copies (I assume, it's about derivative works as well).

From my understanding, one can throw in some non-MIT files or code pieces, but MIT code shall remain MIT-licensed until rewritten or removed.

Can you please point on where I'm wrong?

You are both right. You can relicense MIT, assuming you follow certain requirements, including replicating the copyright notice, but you are not required to give away the source code (even just to the original artifact) at all. The user has to find its own way to the source code.

Replicating the copyright notice for attribution does not imply you are licensing it under MIT. You are following the original license requirements that permit your distribution.