It is hard for me to believe that you heard people saying this, because it would be a dumb thing to say. It's like saying that you use only the hammer (including drilling holes and for changing the lightbulbs), because it's straightforward to use and gives predictable results.
Second, linear regression is not always "interpretable". If you have linear regression model with many polynomial terms, or just a lot of features, it would be hard to interpret. For example, say that you used the raw values of each of the 784 pixels from MNIST† as features. Would knowing that pixel 237 has weight equal to -2311.67 tell you anything about the model? For image data, looking at activation maps of the convolutional neural network would be much easier to understand.
Finally, there are models that are equally interpretable, e.g. logistic regression, decision trees, naive Bayes algorithm, and many more.
† - As noticed by Ingolifs in the comment, and as discussed in this thread, MNIST may be not the best example, since this is a very simple dataset. For most of the realistic image datasets, logistic regression would not work and looking at the weights would not give any straightforward answers. If you look closer at the weights in the linked thread, then their interpretation is also not straightforward, for example weights for predicting "5" or "9" do not show any obvious pattern (see image below, copied from the other thread).