Why should you start lagering? Because you want to make a lager.
It's a simple choice of preference, mate. Why brew a stout? Why brew an IPA? Brew whatever you feel like.
But if the style of beer that you want to brew happens to be a Pilsner, Light Lager, Vienna Lager, Bock, Oktoberfest, Dunkel, Baltic Porter, Schwarzbier, or any variant of those (Maibock, Bohemian Pils, Dopplebock, American Lager, Marzen, Helles Bock, or Eisbock, for example), then you're better off using lagering techniques to achieve certain flavor, aroma, and mouthfeel characteristics.
While lager yeasts are generally described as producing more clean and crisp characteristics than ale yeasts, lager yeasts produce a variety of smells and tastes.
For most styles traditionally made with lager yeasts, you can usually brew a comparable beer with the appropriate ale yeast, but substituting an ale for a lager makes a pretty substantial difference. Most lager styles are defined by flavors and aromas specific to their strains of yeast, so trying to replicate exact characteristics of specific lagers absolutely requires using a lager yeast.
So decide what you'd like to brew. And then decide if you want to invest in lagering equipment and are willing to spend the extra time between brewing and drinking. Maybe you want to match a certain style, or brew an exact clone of a commercial beer, or brew identical wort with different yeasts. But for whatever reason, if you think it's worth the time and money, or if you just enjoy the challenge of learning new techniques, then you should start lagering.