Lyn, it may be a regional thing. Fields by me get hayed twice a summer, and different plants are coming up for each haying. This might be different if fields were planted in grasses specifically for hay. If we baled our field, it would have clover early and more bluestem later.
The wheat is only cut once, and a few wheat seeds do remain in the straw, and wheat is a royal pain to pull out of flower beds!
I have learned the hard way that hay gives me weeds, and straw gives rodents and snakes a shelter. I am horribly allergic to molds, so I try not to handle straw that has mold on it.
I am very glad I can get free wood chips for mulch. If I didn't have that, I would be buying cedar mulch in bags. Without mulch, I would be hoeing weeds and watering constantly.
Actually in most beds, I have planted so intensively that ground covers take the place of mulch. I use a low growing Sedum that doesn't root deep and doesn't require much water and that helps a lot.
Pork pal, I never thought about alfalfa pellets having seeds in them. I guess I assumed they were ground too fine. Most likely, the alfalfa I was fighting was from plants that were there before the bed was created. I didn't till deeply enough to get the roots out. The alfalfa from seed I hoed out with the the other weeds.