That pot is way too big to be starting in, for one thing. Jiffy pots/peat pucks also kind of suck. You want something that gives about 4 inches for the tap root to emerge happily. Plastic solo cups with a hole drilled in the bottom also do fine, but I wouldn't use anything bigger than that.
You don't want your soil to be constantly wet and soppy, and part of that has to do with soil that drains improperly and becomes compacted. If you used smaller containers you would be able to water them properly... in my opinion only using a spray bottle is a horrible idea. The proper way to water is until you see run-off, then you wait until the top is drier and the container is lighter. Planting seeds at the correct depth is also important, half an inch is good so they should stay moist enough even as the immediate surface dries out a little. The matter is really that plant roots breath oxygen, which doesn't dissolve well in water. With a good soil mix and proper wet/dry cycle you'll be facilitating gas exchange, drawing oxygen into the soil. If your soil isn't properly amended and is constantly wet then plant roots will indeed suffocate.
But...if all you ever do is mist the soil surface with a spray bottle you're not watering properly.
Use a decent mix conducive to seed-starting like light Sunshine Advanced #4 or Light Warrior in solo cups and water them properly.
