The second method is the do nothing, ala Natural Method. Just do nothing. The new growth morphs up as the old growth lays over and decomposes. The process takes months and months and in fact, never ends. On some plants in the garden, I can still see the decomposing leave & stem from last years turn.
Both schools work. Both schools are good. It just depends on your preferences. The manicured, clean bed look or the seasonal charm, ala natural. We love them both.
And if you can't reach them with a lawn mower........you can trim them by hand.