I was thinking about this post today as I was driving and the scripture came to me:
John 4:23
23 But the hour cometh, and now is, when the true worshippers shall worship the Father in spirit and in truth: for the Father seeketh such to worship him. (KJV)
These true worshippers are ones where the worship comes out of the heart: It is not mandated, it is not controlled, it is a response that comes from the heart.
Contrasting this with the Old Covenant God told them how to worship Him through the law. It included many aspects of which one was in sacrifices and offerings.
Under the guidelines of how to worship there were MANY sacrifices, many offerings, the tithe and the first fruits it seems to be an endless cycle of giving and sacrificing.
Using your illustration of how the "rule" has been abolished because of the relationship we know from scripture that God does not change.
So while He is now looking for someone who will worship Him without a law, He has given us in the law an example of how He desires to be worshiped.
How can we who have the benefit of the shed blood of Jesus think that we could worship LESS than those who lived under a lesser covenant.
If God desired such a high level of sacrifice and giving without the cost of Jesus blood I could only imagine His desire as in a "level of worship" would be much higher.
We American Christians think that because we spent three or four hours in church on Sunday and an hour and a half in church midweek, dropped $20, $50 or even $100 in the plate that we have adequately honored and worshiped our Master.
If the average Christian would be honest and calculate the actual time spent in Word, prayer, and evangelism they would find that most spend less than 5% of their time pursuing the purposes of the King.
If that same average Christian would calculate the actual percentage of their giving to their gross income most give less than 5% and most tithers give less than 15%
To maintain a full time job you will commit at least 24% of your life to hold that position.
If you sleep only 6 hours per night you contribute 25% of your life to sleeping.
The honest truth is most Christians contribute more to Hollywood than to God spending valuable time watching stupid shows (I'm not against TV either).
True worshipers will worship GREATER than those of Old.