# Is it useful to use sparse regression (e.g. Lasso) when the number of observations is significantly larger than the number of covariates?

I'm learning about penalized/sparse regression and I noticed that the examples used for penalized/sparse regression, e.g. Lasso, are usually cases where the number of observations is significantly smaller than the number of covariates/independent variables/predictors, $$n << p$$.

I was wondering if it would still be useful to apply such methods to datasets where we also have a large number of $$p$$ but the number of observations $$n$$ is significantly larger, $$n >> p$$.

For reference, we have a dataset that has $$n = 19,051$$ observations and each observation has $$p = 336$$ predictors.