I think I understand your question to be leaning more towards philosophy, however the question works in a broader sense as well, so I'll answer the basic question as worded in the heading, "Why are Melochos based on the construction of the Mishkan?"
The simplest answer to this question is that the Mishkan needed to be constructed almost entirely from scratch, making it a perfect model of creating something for the purest motivations, which is nonetheless prohibited on Shabbath. When the Torah tells us, in a nutshell, "Build my tabernacle to all its specifications, but make sure nobody violates the sabbath," we understand that construction of the Mishkan itself, despite its heavenly goal, is prohibited on Shabbath because of the types of creative labor that are involved. Essentially we read the command as, "Build my tabernacle, but not on Shabbath." Then our Mesorah tells us specifically which activities were done that are prohibited, outlining for us what we may not do on any given Shabbath.
See more here: "The Relationship between Shabbat and the Construction of the Mishkan" by Rabbi Michael Rosensweig (Rosh Yeshiva at Yeshiva University)