I’ve built a small, Japanese-style toolbox with poplar, and it has held up fine. Of course, a lot depends upon how it’s used. Both poplar and white pine are similar in their hardness (or lack thereof), and are similar in density.
The advantage of pine or poplar is that they are light. A harder wood like, say, Sapele will typically quite a bit more dense, and the large joiner’s tool chest (especially with all the tills) made from it would be quite heavy even before you added the tools. I believe the joiners toolbox has a skirt around the bottom, which will help protect the main carcase. The biggest disadvantage IMHO is the inevitable ding while a panel is sitting on the bench waiting to be assembled tends to dent the softer woods. Finally, the low cost of poplar is attractive for a workshop project.
The weight is probably less of an issue for the smaller tool chest (for which I believe Paul did use Sapele). Paul didn’t paint his, but that doesn’t prevent you from painting yours if you prefer.