I have noticed the same problem with peat pots and even more with cow pots (made from sanitized cow poo). I had not diagnosed what was going wrong, but wicking the moisture makes a lot of sense. Even using paper pots I make at home is worse than the little plastic seed starter trays or pots. I clean and reuse these, so it's not so bad for environment or my purse. I love the idea of planting the started plants right into the ground without disturbing them by unpotting them ... and I really, really wanted cowpots to be great. But they just do not work very well, neither peat nor cowpots. Sigh.
I have grown beets, only in growbags. My beets did not get very big roots. Maybe I need a different soil mix to encourage more root growth?? Same with carrots. I thought using nice, soft, non-compacted soil in a growbag would be great for root veggies. I also tried both in a large grow container I have mainly for strawberries, with same results. I will try both again this spring, and hope for better results! Thanks for this thread!