I beg to differ. If you do it right, you'll not have much problem with weed seeds. I've done it with both hay and straw. There are those out there, myself included who think that hay bales have a higher availability of nutrient b/c of the diversity of plant material in a bale of hay compared to straw. When you start out, you season the bale by wetting it and giving it a heavy load of nitrogen. this starts the nitrobacter cycle going in the bale, and the temp will quickly rise to 135* or more. You need to keep wetting the bale, and adding nitrogen (I forget how much or how long you keep adding the nitrogen, but you can google this). The bale will be ready to plant when the internal temp drops. It should take at least 2 weeks to complete the process. This process kills a lot of the seeds in the middle. You will still have seeds, but when you cover the top of the bale with your potting soil, and then plant, the seeds at the top should be deep enough that they won't be much of an issue. Your crops should be growing quick enough that they will shade out any seeds that do manage to sprout.
For years, I've used hay as a mulch in my garden. Yes, it does have weed seeds. But, if you mulch properly, it's not an issue at all. (If you keep it thick, the weeds won't sprout, even after years of mulching with hay.) Mulch gets thin, and weeds will sprout. I don't consider this to be a problem at all. Just let the chickens into the weedy area, or toss more hay on top of it. Weeds are a green manure crop as far as I'm concerned. You might want to check out any of the excellent materials written by Ruth Stout on gardening under hay mulch. Most recently, I'm converting my garden to Back To Eden approach to give it even more benefit from permanent mulch.