If learning in Kollel is against the Chazals about Melachah and Derech Eretz, then so is being a Rebbi or a Rav. See the Rama YD 246:6. He brings your Chazals and says that therefore nobody can be a paid Rebbi or a Rav either, since he relies on the congregation. But then he brings dissenting opinions, and rules that the custom is that Torah scholars do benefit from their learning, by support from the community.
Then he brings other opinions that the community should support its Torah scholars even to the point of affluence.
The Rama then says it is a Midas Chasidus – praiseworthy – for someone who can become a Gadol B’Torah and make an independent living, but continues that not everyone is capable of this. It is clear that he is saying that if you have a choice between becoming a Godol B’Torah or making a living, becoming a Godol B’Torah comes first.
As an aside, the Halachah is that you are nowadays allowed to live off Tzedakah to learn (see the Ramah and Shach in Hilchos Talmud Torah.)
The Halchah as expressed by the Rambam which states that anyone who so chooses may learn in Kollel. See also YD Laws of Talmud Torah 246:21 and Shach ad loc. Also, Shulchan Aruch Hilchos Toalmud Torah, in the Shach ad loc, says that nowadays learning all day is the ideal, and that if someone has the ability to do it, he should. The Shach adds that regarding learning all day in general, nowadays we cannot reach our potential in learning the way the Rambam etc. did, since we are not on that level. Therefore, we should learn all day if we can.