Sharon, you said,
thats why they are called ground covers that grow where nothing else does - periwinkle, lily of the valley, etc.
Groundcover isn't called groundcover because it will grow where nothing else does, or seems to. The definition of groundcover from Botany.com
https://www.botany.com/16.gr.htm
GROUND COVER: Refers to low-growing or trailing plants that are used to carpet the ground, as underneath trees or as an overplanting for bulbs.
You said,
So I guess what I got to say is there is no plant that is invasive unless its unattended
That isn't true at all. If you remember the trumpet vine thread, this plant is native to North America, but can be invasive in the garden due to it's extensive and tenacious root system. I tended to the ones that I inherited every year, yet they invaded all over the garden from underground roots. Some plants become invasive from their seeds spread by birds, mammals, or wind while others can be invasive from their roots. The definition of invasive from Webster's dictionary
https://webster.com/dictionary/invasive
2 : tending to spread; especially : tending to invade
3 : tending to infringe
As far as the plants in question being tended to, there is no guarantee that will happen. People sell their property to other people that may not care for the plant material or have the knowledge of what to do to keep it contained. Others plant something and don't realize that it can be invasive. I have a friend who owns a large expanse of wooded property with a stream. His landscaper planted periwinkle aka vinca around the mailbox and it has escaped. It is now growing out of control in the wooded stream area, smothering other native plants such as woodland ginger. A large Japanese honeysuckle would need every berry removed so the birds don't spread the plants. If it's growing on a pergola where the top can't be reached for constant pruning, it can, and will be spread by the birds.
In some situations I recommend groundcovers that form clumps and do not spread by roots, runners or seed. I'm not saying to only plant natives, but that consideration should be made for plants that won't invade the environment where it's planted.
Here are some selected quotes from Invasive.org which is a joint project of The Bugwood Network, USDA Forest Service and USDA APHIS PPQ.
https://www.invasive.org/eastern/
A biological invasion of non-native plants is spreading into our nations' fields, pastures, forests, wetlands and waterways, natural areas, and right-of-ways. Variously referred to as exotic, nonnative, alien, noxious, or non-indigenous weeds, invasive plants impact native plant and animal communities by displacing native vegetation and disrupting habitats as they become established and spread over time.
Some of the plants on this list are often found in ornamental plantings and landscapes. In fact, many non-native plants introduced for horticultural and agricultural use now pose a serious ecological threat in the absence of their natural predators and control agents. This publication will aid landowners, foresters, resource managers, and the general public in becoming familiar with invasive plants in their area to help protect our environment from the economic and ecological impacts of these biological pollutants.
You said,
The best way to grow a trumpet vine is up a post or dead tree stock and pruned every year
I refer you to this thread where I posted on May 16, 2006 and December 7, 2006, and explain all about this native that CAN be invasive.
https://www.helpfulgardener.com/forum/viewtopic.php?t=1735
Here is the USDA (United States Department of Agricultural) site, with a map, that lists where this plant is invasive.
https://plants.usda.gov/java/nameSearch?keywordquery=campsis+radicans&mode=sciname&submit.x=0&submit.y=0
If nurseries didt sell plants they would go bankrupt.
There is the point of ethics. Selling plants that are invasive is not ethical. Many nurseries sell Japanese honeysuckle and it's listed as an invasive, but they sell it anyway. Many nurseries sell plants, stay in business and don't sell known invasives.
Here is a link to find DNR (Department of Natural Resources) home pages for the United States and Canada. https://www.walleyehunter.com/dnrmap.html
You said,
Sub phlox, pachysandra, lamium, periwinkle are a few that come to mind right now" (spelling corrections made by moderator).
By "Sub phlox" I'm thinking you mean Phlox subulata, of which there are several varieties. Here is the USDA (United States Department of Agricultural) site, with a map, that lists where this plant is invasive.
https://plants.usda.gov/java/profile?symbol=PHSU3
Pachysandra we've discussed before on another thread. There is a native that is NOT invasive and a non-native that is.
Pachysandra procumbens aka Allegheny spurge is native and is NOT invasive.
Pachysandra terminalis aka Japanese pachysandra is NOT native and can be invasive. Here is the USDA (United States Department of Agricultural) site, with a map, that lists where this plant is invasive.
https://plants.usda.gov/java/profile?symbol=PATE11
Lily-of-the-valley aka European lily-of-the-valley aka Convallaria majalis is also considered invasive by the USDA. Here is the USDA (United States Department of Agricultural) site, with a map, that lists where this plant is invasive.
https://plants.usda.gov/java/profile?symbol=COMA7
American lily-of-the-valley aka Convallaria majuscula is considered threatened in these areas by the USDA.
https://plants.usda.gov/java/profile?symbol=COMA19
There are native and introduced varieties of Lamium. Natives are Lamium album aka white deadnettle, Lamium amplexicaule aka henbit deadnettle, Lamium maculatum aka spotted henbit and Lamium purpureum aka purple deadnettle are natives so you need to know which one you are purchasing and planting to know if it's invasive.
Here is one of many site where you can search to find what is invasive. There are many helpful links here.
https://www.invasive.org/
Newt