As far as I know, we don't check the coefficient significance in Lasso and elasticnet models. Is it because insignificant feature coefficients will be driven to zero in these models?. Does that mean that all the features in these models are significant? Why are we not checking the significance of the coefficients in Lasso and net elastic models?.
Generally, regression models are regularized with Lasso, Ridge, or Elasticnet to improve predictive performance. Predictive performance is different than statistical significance. Predictive performance is more about the entire model than any single coefficient. Checking for the statistical significance of an individual coefficient will not impact predictive performance.