Besides the extremely thin atmosphere on Mars and construction obstacles, there are two other reasons to not build a landing strip on Mars that I can see.
Why go to the same place twice?
Mars is big. It's not as big as Earth, but there's still a whole lot of unexplored terrain that would be of interest to study. By building a landing strip, even if you can build one and it's viable in the first place (which, given the other answers so far, appears highly doubtful), you commit significant resources to a single location. Just like you can't get a good idea of what the Earth looks like by studying only Manhattan or the Mariana trench, missions have deliberately picked highly disparate landing sites at least in part precisely to study different parts of Mars to get a better idea of the planet's overall geology.
Landings aren't precise enough
Our Mars landings just aren't precise enough for a landing strip to make sense. You are probably thinking in terms of doing this:
while reality is like this:
Look at that 2012 Curiosity landing. A landing ellipse of 12 x 4 miles, or 19 x 6.5 km, with touchdown 2.4 km from the centre, is far too imprecise for a landing strip to make any sense. Not only would you have to actually land on the landing strip in the first place; for a horizontal landing onto a landing strip to make any sense at all, you have to be going in just about exactly the right direction when you hit the ground, and hit very close to the correct spot on the landing strip. We aren't talking a few kilometers here; we are talking more like on the order of tens to a few hundreds of meters.
We simply aren't there yet, and I wonder if we will ever be there before we have significant human presence on Mars, at which point there's more productive things for those people to do than flatten and cover a large swath of Mars surface near their base where it is most accessible for study.
The Space Shuttle was able to do that kind of landing, but it did so on Earth (with an atmosphere hundreds of times thicker, with corresponding differences in aerobraking and lift capability), and it had significant constraints on landing. There's a reason why the deorbit burn was called a landing commitment.