It is true that only schematics versions of 'life problems' lead to general mathematical theory. However: (a) the students bring 'life' into the classroom with them. (b) the process of moving from life to the APPROPRIATE' schematic is part of mathematics (applied mathematics).
Isn't there room for some movement in the class which involves some 'life' (open-ended messy problems of potential complexity) and the theory? Even when I think I have already done this - I have been struck by what happens when students ('good students') try to work back from the theory to a real, physical example. The experience reveals a lot of misunderstanding. The learning which happens then seems essential to a well-rounded course of mathematics.