Insertion shots are great. However, most trainers follow strictly upon one school of striking or the other and almost completely ignore insertion shots as they're usually considered foul shots. Not many pure striking contests will both punches and elbows (boxing, modern kick boxing). And those that allow that, may not allow a lot of other insertion shots that are widely available in a clinch situation like poppers, forearms crams, shoulder shrugs etcs.
But if someone were to earnestly train a striking game with insertion shots as part of their repetoire, I believe they would have a wide variety of striking tools available for them in every situation they're in.