I've smothered some pretty tough customers, definitely mint, nutgrass, & Bermuda... asparagus fern, bahiagrass, baby walnut, oak & pecan trees, wild berry & honeysuckle vines, Nandina, Vinca major, Conoclinium, Allium canadense, Chinese elm, and countless others whose names will never be known. Success rate to date = 100%. Without light, any plant will die once it has exhausted its' energy reserves.
I didn't get the impression there were any notoriously difficult species like Houttuynia cordata in question in this discussion. But if any shows up in my yard, I have no doubt that I can smother it if, for some reason, I don't notice that it's sprouted for so long that it can't be pulled out.
Once smothered, an area is pristine. Nothing is growing there. Digging a hole to plant something can cause a buried seed to be able to sprout, (which would be noticed by me & pulled,) but aside from that, any new sprouts from wind-blown or critter-dropped seeds would be on the surface. Easy to notice & pull (or just add another smother layer if it's a whole outbreak patch of something.)
Annual weeds should only be a problem once. Pull, mow, or smother before they create & drop the next years' crop of seeds. Break the cycle. I've never had any problems with seed-weeds like that because I always start a new bed with cardboard, then pull anything voluntary, that I didn't put there. Maintaining a clean slate would be much more difficult if not starting that way.
For years, (until we moved this past April,) this is what was on the other side of CL fence, upwind most days. There were definitely unwanted sprouts on my side, but I never spent more than 5-10 minutes per week patrolling, pulling as I walk around the yard and enjoy/inspect the plants.
Yes, organic mulches/smothers deteriorate, are not permanent, but I've never heard of an alternative barrier that IS permanent besides paving the spot. After doing it for about 30 yrs total in 2 diff states, I recommend smothering/mulching because it's free, incomparably easy, improves the ground, & I know it works. Every fall, I rake leaves onto the nearest bed area to keep things going:
http://permaculturenews.org/20...
I love the way all of this coincides with spending the least amount of time, effort, and $ in regard to maintenance. For me, all 3 of these things would best be spent on the more fun parts of gardening, buying & manipulating the plants, so whatever methods can do that for me are what I use. I share so enthusiastically and in such detail because I would never have the ability to have "flower beds" or maintain a mowed yard without doing these things, something about which I'm very passionate and exuberantly enthusiastic because of the results I've seen. I'm a person of very small stature, very little strength, and until a few yrs ago, a single mom with full-time job. I wish everyone the best in finding the methods that work as well for them, and to achieve a comparable state of satisfaction with their yard/garden.
No weeds, just plants with a purpose. One of my favs, from when I lived in OH, about 13 yrs ago. I did buy some mulch to get this going.