Yes, I think you will live to regret it if you plant phleum pratensis or Timothy grass in your houseplant pots. This grass is persistent outdoors, may spread rapidly in the pot, or not grow very well for long indoors, and likely won't make an attractive looking composition. As for why you don't often see 'groundcover' plants in houseplant pots, that's because the pot used is of a suitable size for a single houseplant and there is insufficient soil to give root room for more than a single plant, whereas outdoors in open ground, no such restrictions are present.
Sometimes people may plant more than a single plant in a large pot, perhaps a low growing type combined with a taller, narrower type to make an attractive composition, and this can work quite well if the pot shape and plants concerned have been selected carefully with their growth habit, rate of growth and eventual size in mind. Regardless, eventually, they will need to be separated and potted individually as they get larger and require more root space.