it should default to the interior point solver but does also have iteratively reweighted least squares. The first hopefully matches quantregs default as it was programmed up according to the article (The Gaussian Hare and the Laplacian Tortoise).
Anyway yeah, it’s all about use-cases. The usecase in OP is quite performance sensitive though, and does require sparse liinear algebra to be acceptable. I know because I’ve estimated these models quite a few times with quite a few individuals. Using the penalized version of Koenker and also the plug-in estimator by (striking out on the author here).