I think it is a good method, except once my seeds break the soil or growing medium I get the plastic off ASAP, to avoid disease.
I suppose that might depend on how humid your place in TX is, and you can bet it is always humid here. But for $5 at Walmart you can also get a clear cover pluse 1020 tray for seedlings with plug inserts from Walmart which is what I used to use.
It depends if you prefer to transplant at that stage (a ~ 1" x 1" x 1.75" plug). I do. Starting directly in a 3" round is certainly a better plan and probably what the experts here wil recommend, but I use lights and simply don't have the room. I don't know how many seeds you are using, but I use only one or two per plug and select the best to plant before moving up to the pot (recycled yogurt container). I am sure every approach has it pluses and minuses.
Recently I did something similar to you ... got a cake cover (free from the nice lady in the Walmart bakery ... she mentioned if she gave me the bottom she would have to charge since that is what is counted for sales purposes
) to use as a greenhouse for some seeds, Litchi Tomatoes, since they are a real beach to germinate quickly. Actually I tried them 4 ways, and nothing sped them up in my trial. It made no difference since after a month and a half they got some secret message all of them germinated magically together. Hope that helps for yours.