I start some seeds in Jiffy and other peat pots. Roots not only break through easily, they already had with the seedlings only a few weeks old.
They do lose water faster for sure, but it just means I give them more water (daily watering cycle scaled back to every other day if in close quarters so water loss decreases).
One initial problem if you cover the top with plastic to reduce water loss is the tendency for mold to grow. A spray with 1:10 solution OTC hydrogen peroxide to water wipes out the mold in an application or two.
One issue is supposedly certain plants like peppers don't like the more acidic pH of peat, or peat pots, but our tapwater that I use to water is a bit alkaline so it seems to not be much of an issue here.
One positive aspect is I put a small bit of dirt in a plastic tray before setting the pots in it, and keep that dirt moist. It encourages more root growth than I'd otherwise have in the same size plastic or other unpermeable containers. Many end up with roots coming out the bottom that are longer than the plant is tall for the first few weeks. The roots can get a bit tangled and broken when it is time to separate them for planting but I feel I still end up with more roots than I otherwise would in the same amount of space.
Overall I can take them or leave them though, I also planted in plastic pots and used same seed starter soil and don't see any significant difference in growth rate "yet", but the plastic pots are larger so eventually that factor will weigh against the peat pots because I am delayed in putting them outside due to unusually strong windy days this spring.