You can explain things with more than a single picture. You can also play with pictures in your mind, and you can encourage students to do so by giving them more than one picture. Visualizing corner cases is often very useful. For triangles, you can change angles and side lengths and see which facts still hold and which don't and how certain values/function results develop.

Moreover, it very much depends on who your target group is. My brain, for example, works entirely inductively (in the beginning). I won't be able to develop an intuition of something if I don't start with examples. Pictures are often good examples. During my undergrad studies, my linear algebra prof was as critical about pictures as you and other commenters here. I hated it. I was never able to get an intuition about the more abstract topics until I saw concrete examples including pictures in later lectures and projects. Moreover, not everyone is going to be a theoretical mathematician or quantum physicist. I suspect that by not showing pictures, you usually lose more students along the way than pictures would ruin students that need a fully abstract understanding (later). It would be interesting to see some data on this, but I guess its going to be difficult to collect.