Why keep taharat hamishpacha?

Yes, you are allowed to touch once you are married. In fact, you are supposed to enjoy the physical side of the relationship with your spouse – whenever you aren't niddah. Sexual abstinence for married couples while the wife is niddah is explicitly mandated in the Torah (see Vayikra 15:19 and 18:19), and remains just as important as it was before you got married.

You ask why we need to keep the laws of taharat hamishpacha. The simple answer is because the Torah says so, and, as is usually the case, the Torah doesn't present us with detailed explanations. Certainly the guidelines for sexual relations within marriage are consistent with the Torah's approach of limiting and elevating physical pleasures. For example, we are almost always permitted to eat, and are required to do so on Shabbat, Yom Tov, etc. But we are not allowed to partake of non-kosher food, or milk with meat, and we need to make brachot before and after eating. Similarly, the physical relationship is considered holy, and is a central component of marriage – within the Torah's parameters. Rabbinic sources, and couples who have kept these laws over decades of marriage, also suggest that the taharat hamishpacha framework (although it can be challenging at times, especially at the beginning) ultimately enhances and renews the marriage relationship.

You might enjoy Rivkah Slonim's book, Total Immersion (published by Urim). It presents essays and anecdotes by different authors who approach the topic from a wide variety of perspectives.