Is there ever an advantage to using a light-bottomed pan?

Firstly, light-bottomed pans exist partly because they save cost and weight (the latter being relevant for, say, taking a pan when hiking). However, there are applications for which a light-bottomed pan can be preferable. These are when you need responsiveness to external heat more than heat retention and evenness. Taking a light pan off the stove will more quickly halt cooking, because it has a lower thermal mass. The pan will also heat up more quickly, but this is less relevant when compared to a properly preheated, thicker pan.

This article goes into some detail on considerations for pan selection. Crucially:

For sautéing and other cooking that calls for quick temperature changes, a pan should be responsive. This means that the pan is doing what the heat source tells it to, and pronto. For example, if you sauté garlic just until fragrant and then turn down the flame, the pan should cool down quickly so the garlic doesn’t burn. Responsiveness isn’t as crucial for boiling, steaming, or the long, slow cooking that stocks and stews undergo.

Additionally, as mentioned by @Blargant in a comment, while responsiveness is less relevant in situations where a relatively large amount of water is used, the positive properties of a thicker pan are also less useful in those cases. Thus, cost becomes a concern, which is why commercial stock pots and the like tend to be thin.