my missus gets tempted by thyme plants every so often and keeps them in pots on the patio. Then they start to fail and she throws them out. I have about four around the garden that I rescued and planted out, and they thrive. I think they need to make deep roots, where they grow naturally the 'soil' is a gravel layer on rock, the gravel holds almost no water, but there is melt water running over the rock underneath it. It is a strange combination, dry on top and cold and wet at the bottom, most plants can't handle it, but it is thyme's natural habitat. I think my created, draining, soil on top of heavy clay sort of imitates it. Most of the year if I dig a hole a couple of feet deep into the clay it will fill with water.
I would add Marjoram and oregano to that list, they are common names that seem cover a number of plants, and sometimes seem to be used interchangeably, but they are probably the most used in our kitchen, followed by mint and chives. It is worth removing the flowers from chives, they say it means they hold their flavour, it also means they don't produce seeds and grow out of every crack and crevice.