Tithing has always been a big subject in the church. I do not think I have attended a church that a tithing sermon didn't happen every few months or so. A whole sermon, just about tithing. One of the things never mentioned though is this section of Deuteronomy though. Where God explicitly states what is to be done with a tithe. All of it didn't go to "church leaders", the majority of the time, it was still yours. You still ate your tithe offering, you just didn't eat it at home. You took it to the tabernacle or the temple and offered as a sacrifice to God. It had to meet the requirements as laid out, but then you ate it. Every three years, instead of you eating it, you gave it away to those that need it.
I am not pointing this out to say the current system of tithing is bad, but it is not what is prescribed. I believe the current system is based on Abraham and Melchizedek in Genesis 14. In their meeting, Abraham gave Melchizedek a tenth of everything and it states that Melchizedek was a High Priest of God. However, there wasn't just two people at this meeting, there were three. The king of Sodom was there, too. After giving a tenth to Melchizedek we see that the king of Sodom turn down (preemptively or otherwise as we don't know) what was being offered and saying he only wanted the men. Was this a tithe, too? Neither are mentioned as being a tithe. The first mention of a tithe in the Bible is Leviticus 27:30 - where it talks about what you can do if you wish to redeem some of your tithe. Again, something that the current system doesn't really allow.