Do old roots need to come out before a new planting?

If I don't pull the old plants out (roots and all), can the new plant grow?

Square Foot Gardening style: In April, I put 4 Chard in a square. In mid/late July, I'd like to start a Kale for fall/winter harvest. I'd like to plant the Kale in the middle of the square and eat the 4 Chard later - when the Kale is out of the ground and can use some sun. Can this be done... will the dead Chard roots interfere with the new Kale roots?

Thank you.

The old root ball of plants increase soil carbon, soil microbes, and helps water inflow. They also kickstart new seedlings by the transfer of the microbes.

So, other than digging in some manure, compost and/or blood & bone to replenish the nutrients used by the previous crop, I suggest just leaving the old roots in situ.

You may even get a reshoot from the old stumps = bonus!

Also, if there are any gaps, there's alway the opportunity to cram in a few other quick maturing leafy greens like lettuce, etc to take advantage of space and the available nutrients.

I always think of old roots as a form of precompost already perfectly mixed in the soil. Herbaceous roots decay quickly while providing food to attract earthworms and beneficial microbes into the garden.

When I can, I will plant a new tree next to the stump of an old one. I always hope to get some of the benefits of hugelculture without the work. On top of that, new roots can take advantage of the paths that the older tree has already forced into the limestone bedrock under my soil.