There are choices for calling-and-texting focused mobile phones, though most of those fit more within the feature phone space than the smartphone one. Nokia has a wide range of throwback models that use classic form factors such as the 2660 Flip that are mostly just call-and-text devices, though they often have a few other functions on board as well.
There is another approach you could take with an Android phone if all you ever wanted was calls and texts. Android lets you remove or at least hide most onscreen icons, so you could set up an Android phone so that it appeared to only offer calls and texts, if that's all you ever wanted to look at.