Rooting your phone or tablet gives you complete control over the system, and that power can be misused if you’re not careful. Android is designed in such a way that it’s hard to break things with a limited user profile. A superuser, however, can really trash things by installing the wrong app or making changes to system files. The securitymodel of Android is also compromised to a certain degree as root apps have much more access to your system. Malware on a rooted phone can access a lot of data. Again, you need to be careful what you install.
For this reason, Google does not officially support rooted devices. There’s even an API called SafetyNet that apps can call on to make sure a device has not been tampered with or compromised by hackers. A number of apps that handle sensitive data will do this check and refuse to run on rooted devices. One of the most prominent examples of this is Android Pay — it cannot even be opened on devices that fail the SafetyNet check. If losing access to high-security apps is a big deal, you might not want to mess around with rooting.
Root methods are sometimes messy and dangerous in their own right. You might brick your device simply trying to root it, and you’ve probably (technically) voided your warranty doing so. Depending on the company, you might still be able to get a device repaired if you damage it attempting a root, but that’s not a guarantee.
Starting in Android 5.0 Lollipop, system updates for some phones (like Nexus and Pixel devices) will only work on stock unrooted devices. This is because of a change to the way Android processes the OTA file. Updates now patch the entire system directory as a single blob, so any changes or extra files (i.e. root) will throw off the verification and the update will abort.
On other phones and tablets, virtually every OTA update you get will wipe out root and block the method from working again. If having root access is really important to you, you might be left waiting on older buggy software while you beg for a new root method or a modded OS update.