The rooting of your phone or tablet gives you total control over the system, and this power can be misused if you are not careful. Android is designed so that it is difficult to break things with a limited user profile. A superuser, however, can really trick things by installing the wrong application or making changes to the system files. The Android security model is also compromised to some extent because root applications have much more access to your system. Malware on a rooted phone can access a lot of data. Again, you have to pay attention to what you are installing.
For this reason, Google does not officially support rooted devices. There is even an API called SafetyNet that applications can call to ensure that a device has not been tampered with or compromised by hackers. A number of applications that process sensitive data perform this check and refuse to run on rooted devices. One of the most striking examples is Android Pay – it can not even be opened on devices that fail the SafetyNet check. If losing access to highly secure applications is a big problem, you may not want to go wrong with rooting.
Root methods are sometimes messy and dangerous in themselves. You can brick your device by simply trying to root it, and you've probably (technically) voided your warranty by doing it. According to the company, you can always repair a device if you damage it by trying a root, but this is not a guarantee.
Starting from Android 5.0 Lollipop, system updates for some phones (like Nexus and Pixel devices) will only work on non-stored devices. This is because of a change in the way that Android processes the OTA file. Updates now fix the entire system directory as a single blob, so changes or additional (root) files will cancel the check and the update will cancel.
On other phones and tablets, virtually all OTA updates will be erased root and block the method from working again. If root access is really important to you, you might have to wait for an old buggy software while you request a new root method or a moderated update of the operating system.