Your restrictions are quite limiting. But never the less, for a linear expression, you can definitely do something.
I have had my student write stories for an expression. So something in like
3x + 4y - 5
You could say that $x$ represents the number of oranges and $y$ the number of apples. The students could write something like:
Joanne sold $x$ oranges for \$3.00 each, $y$ apples for \$4.00 each, and \$5.00 were stolen from the till
and for a different expression
6x + 7y -3y +18 -2x -23
the students could come up with a story like
Jim sold $x$ apples for \$6.00 each, $y$ oranges for \$7.00 each, bought another $y$ oranges for \$3.00 each, found \$18.00 lying on the ground, bought $x$ apples for \$2.00 each, and spent \$23.00 for a new kitchen table
So maybe they're hoakie. But now we can ask, "Who has more money? Jim or Joanne? Explain your answer."
There are all sorts of variations on this. What I'd stress here isn't an application of simplifying algebraic expressions, I'd stress that expressions can be tied to stories. The more students play with and create these sorts of stories, the less intimidating word problems are for them. But it does take a lot of work. And, it takes a lot of convincing to get them to realize what is and isn't a good story. At first, many of their stories will be nonsensical (I'm assuming you're teaching high school or junior high school students).
OK. So there's an application---contrived as it is---that you could use in your class. But, if you allow graphing and the students have spent some time working with quadratic equations, then you have a lot more room to show the importance of simplifying.
Here the context is to talk about scientific exploration/inquiry. If you develop a theory, you might be inclined to express the relationship between two quantities in one form, but after collecting data, it might be more sensical to present a relation between the two quantities differently.
You can present a situation where two different people have come up with two different expressions:
Kate came up with the following equation for one set of data
y = (x+2)(x-4)
Ken had a different set of data and wrote out the following equation
y = (x-1)^2 - 9
Now provided you've talked about graphing, zeroes of polynomials, and the vertex of a parabola, then you can talk about a context where simplifying can answer questions. You can ask, "Could the data Ken and Kate collected come from similar experiments?" Just looking at the data wouldn't suffice since the data sets are different. But, if the students know how to simplify the expressions, then they
can answer the question.
Granted you might feel you want a clean example when first presenting the notion of gathering like-terms and simplying expressions. But sometimes, you just don't have enough to work with yet to make the point. It's important to teach your students that there isn't always an immediate answer to why we do something. But then promise them that you'll revisit the idea in a few weeks when they've developed some more skills and a few more ideas. If you're good to your promises, in my experience, the students will often play along.
In all of this, long range planning is important. You need to know what skills and knowledge base you're starting with in your students; how you plan to build on that; and, where you intend to get. Sometimes, to create interesting and convincing "real world" applications, you have to be creative in how you present the material in the first place.