E. peplus isn't indestructible. It's a prolific seeder, so will germinate any time you disturb the soil and give it some bare ground to grow into. But it's an annual, so it'll die after flowering, and doesn't put down a big root system, so is quite easy to pull up.
E robbiae and E cyparissias, which spread by runners, are more difficult to control. But they self seed a lot less readily.